Pub Date : 2025-01-14DOI: 10.1016/j.jalgebra.2024.12.025
Xiaokun Zhong
Let be a fibred surface over an algebraically closed field k of characteristic , where S is a minimal smooth projective surface of general type and B is a smooth projective curve of genus . We prove that the group of fibration-preserving automorphisms of f has order at most . Furthermore, we provide an example to show that the exponent 4 of the polynomial bound is sharp.
{"title":"Bound of automorphisms of fibred surfaces in positive characteristic","authors":"Xiaokun Zhong","doi":"10.1016/j.jalgebra.2024.12.025","DOIUrl":"10.1016/j.jalgebra.2024.12.025","url":null,"abstract":"<div><div>Let <span><math><mi>f</mi><mo>:</mo><mi>S</mi><mo>→</mo><mi>B</mi></math></span> be a fibred surface over an algebraically closed field <em>k</em> of characteristic <span><math><mi>p</mi><mo>≥</mo><mn>5</mn></math></span>, where <em>S</em> is a minimal smooth projective surface of general type and <em>B</em> is a smooth projective curve of genus <span><math><mi>b</mi><mo>≥</mo><mn>2</mn></math></span>. We prove that the group of fibration-preserving automorphisms of <em>f</em> has order at most <span><math><mn>15658</mn><msup><mrow><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup></math></span>. Furthermore, we provide an example to show that the exponent 4 of the polynomial bound is sharp.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 725-745"},"PeriodicalIF":0.8,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-09DOI: 10.1016/j.jalgebra.2024.11.037
Tom Bachmann
We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2.
{"title":"A C2-equivariant Gabber presentation lemma","authors":"Tom Bachmann","doi":"10.1016/j.jalgebra.2024.11.037","DOIUrl":"10.1016/j.jalgebra.2024.11.037","url":null,"abstract":"<div><div>We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 587-597"},"PeriodicalIF":0.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-08DOI: 10.1016/j.jalgebra.2024.12.021
Atsushi Takahashi , Hongxia Zhang
This paper calculates the number of full exceptional collections modulo an action of the quotient of a group as the set generated by spherical twists for an abelian category of coherent sheaves over an orbifold projective line with a zero orbifold Euler characteristic. This is done by a recursive formula naturally generalizing for the Dynkin case and an abelian category of coherent sheaves over an orbifold projective line with a positive orbifold Euler characteristic.
Moreover, we have another expression of the degree of the Lyashko-Looijienga map for the universal unfolding of a simple elliptic singularity in the Legendre normal form calculated by Hertling-Roucairol.
{"title":"Number of full exceptional collections modulo spherical twists for elliptic orbifolds","authors":"Atsushi Takahashi , Hongxia Zhang","doi":"10.1016/j.jalgebra.2024.12.021","DOIUrl":"10.1016/j.jalgebra.2024.12.021","url":null,"abstract":"<div><div>This paper calculates the number of full exceptional collections modulo an action of the quotient of a group as the set generated by spherical twists for an abelian category of coherent sheaves over an orbifold projective line with a zero orbifold Euler characteristic. This is done by a recursive formula naturally generalizing for the Dynkin case and an abelian category of coherent sheaves over an orbifold projective line with a positive orbifold Euler characteristic.</div><div>Moreover, we have another expression of the degree of the Lyashko-Looijienga map for the universal unfolding of a simple elliptic singularity in the Legendre normal form calculated by Hertling-Roucairol.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 570-586"},"PeriodicalIF":0.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A vertex transitive graph Γ is said to be 2-distance transitive if for each vertex u, the group of automorphisms of Γ fixing the vertex u acts transitively on the set of vertices at distance 1 and 2 from u, while Γ is said to be 2-arc transitive if its automorphism group is transitive on the set of 2-arcs. Then 2-arc transitive graphs are 2-distance transitive. In 2008, the 2-arc transitive Cayley graphs on dihedral groups were classified by Du, Malnič and Marušič. In this paper, it is shown that a connected 2-distance transitive Cayley graph on the dihedral group of order 2n is either 2-arc transitive, or isomorphic to the complete multipartite graph for some and with .
{"title":"The classification of two-distance transitive dihedrants","authors":"Jun-Jie Huang , Yan-Quan Feng , Jin-Xin Zhou , Fu-Gang Yin","doi":"10.1016/j.jalgebra.2024.12.023","DOIUrl":"10.1016/j.jalgebra.2024.12.023","url":null,"abstract":"<div><div>A vertex transitive graph Γ is said to be 2<em>-distance transitive</em> if for each vertex <em>u</em>, the group of automorphisms of Γ fixing the vertex <em>u</em> acts transitively on the set of vertices at distance 1 and 2 from <em>u</em>, while Γ is said to be 2<em>-arc transitive</em> if its automorphism group is transitive on the set of 2-arcs. Then 2-arc transitive graphs are 2-distance transitive. In 2008, the 2-arc transitive Cayley graphs on dihedral groups were classified by Du, Malnič and Marušič. In this paper, it is shown that a connected 2-distance transitive Cayley graph on the dihedral group of order 2<em>n</em> is either 2-arc transitive, or isomorphic to the complete multipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>m</mi><mo>[</mo><mi>b</mi><mo>]</mo></mrow></msub></math></span> for some <span><math><mi>m</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>b</mi><mo>≥</mo><mn>2</mn></math></span> with <span><math><mi>m</mi><mi>b</mi><mo>=</mo><mn>2</mn><mi>n</mi></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 508-529"},"PeriodicalIF":0.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-07DOI: 10.1016/j.jalgebra.2024.12.014
Dinushi Munasinghe , Ben Webster
We study the representation theory of the type B Schur algebra with unequal parameters introduced by Lai and Luo. For generic values of , this algebra is semi-simple and Morita equivalent to the type B Hecke algebra, but for special values, its category of modules is more complicated. We study this representation theory by comparison with the cyclotomic q-Schur algebra of Dipper, James, and Mathas, and use this to construct a cellular algebra structure on .
This allows us to index the simple -modules as a subset of the set of bipartitions of n. For m large, this will be all bipartitions of n if and only if is quasi-hereditary. In this case, the algebra is Morita equivalent to the cyclotomic q-Schur algebra. We prove a modified version of a conjecture of Lai, Nakano, and Xiang giving the values of where this holds: if m is large and odd, for all k satisfying ; if m is large and even, for all k satisfying . We also prove two strengthenings of this result: an indexing of the simple modules when q is not a root of unity, and a characterization of the quasi-hereditary blocks of .
{"title":"On the representation theory of Schur algebras in type B","authors":"Dinushi Munasinghe , Ben Webster","doi":"10.1016/j.jalgebra.2024.12.014","DOIUrl":"10.1016/j.jalgebra.2024.12.014","url":null,"abstract":"<div><div>We study the representation theory of the type B Schur algebra <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span> with unequal parameters introduced by Lai and Luo. For generic values of <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>, this algebra is semi-simple and Morita equivalent to the type B Hecke algebra, but for special values, its category of modules is more complicated. We study this representation theory by comparison with the cyclotomic <em>q</em>-Schur algebra of Dipper, James, and Mathas, and use this to construct a cellular algebra structure on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span>.</div><div>This allows us to index the simple <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span>-modules as a subset of the set of bipartitions of <em>n</em>. For <em>m</em> large, this will be all bipartitions of <em>n</em> if and only if <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span> is quasi-hereditary. In this case, the algebra <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span> is Morita equivalent to the cyclotomic <em>q</em>-Schur algebra. We prove a modified version of a conjecture of Lai, Nakano, and Xiang giving the values of <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> where this holds: if <em>m</em> is large and odd, <span><math><mi>Q</mi><mo>≠</mo><mo>−</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> for all <em>k</em> satisfying <span><math><mfrac><mrow><mn>4</mn><mo>−</mo><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>≤</mo><mi>k</mi><mo><</mo><mi>n</mi></math></span>; if <em>m</em> is large and even, <span><math><mi>Q</mi><mo>≠</mo><mo>−</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> for all <em>k</em> satisfying <span><math><mo>−</mo><mi>n</mi><mo><</mo><mi>k</mi><mo><</mo><mi>n</mi></math></span>. We also prove two strengthenings of this result: an indexing of the simple modules when <em>q</em> is not a root of unity, and a characterization of the quasi-hereditary blocks of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 211-258"},"PeriodicalIF":0.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-07DOI: 10.1016/j.jalgebra.2024.11.036
Daniel Corey , Michael Joswig , Julien Schanz , Marcel Wack , Moritz Weber
Motivated by the vast literature of quantum automorphism groups of graphs, we define and study quantum automorphism groups of matroids. A key feature of quantum groups is that there are many quantizations of a classical group, and this phenomenon manifests in the cryptomorphic characterizations of matroids. Our primary goal is to understand the resulting structures from an algebraic and computational point of view. In particular, we investigate the relationship between these quantum groups and to find when these quantum groups exhibit quantum symmetry. Finally, we prove a matroidal analog of Lovász's theorem characterizing graph isomorphisms in terms of homomorphism counts.
{"title":"Quantum automorphisms of matroids","authors":"Daniel Corey , Michael Joswig , Julien Schanz , Marcel Wack , Moritz Weber","doi":"10.1016/j.jalgebra.2024.11.036","DOIUrl":"10.1016/j.jalgebra.2024.11.036","url":null,"abstract":"<div><div>Motivated by the vast literature of quantum automorphism groups of graphs, we define and study quantum automorphism groups of matroids. A key feature of quantum groups is that there are many quantizations of a classical group, and this phenomenon manifests in the cryptomorphic characterizations of matroids. Our primary goal is to understand the resulting structures from an algebraic and computational point of view. In particular, we investigate the relationship between these quantum groups and to find when these quantum groups exhibit quantum symmetry. Finally, we prove a matroidal analog of Lovász's theorem characterizing graph isomorphisms in terms of homomorphism counts.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 480-507"},"PeriodicalIF":0.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-06DOI: 10.1016/j.jalgebra.2024.11.033
William Giuliano , Alexander A. Ivanov
<div><div>The paper contributes to the classification of locally projective graphs and their locally projective groups of automorphisms. This project aimed to merge sporadic and classical simple groups in a uniform setting. The list of known examples of locally projective groups of automorphisms includes the classical groups<span><span><span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mi>O</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mi>Ω</mi></mrow><mrow><mn>8</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo><mo>:</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>3</mn><mo>)</mo></math></span></span></span> as well as the sporadic simple groups<span><span><span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>22</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mn>23</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mn>24</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>H</mi><mi>e</mi><mo>,</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>J</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>B</mi><mi>M</mi><mo>,</mo><mspace></mspace><mi>M</mi><mo>,</mo></math></span></span></span> where <em>M</em> is the Monster sporadic simple group, the largest and most famous sporadic simple group. The locally projective graph for the Monster gives an important insight in the structure of 2-local subgroups in the Monster. The list also includes some remarkable non-split extensions which probably would not be discovered otherwise:<span><span><span><math><msup><mrow><mn>3</mn></mrow><mrow><mn>7</mn></mrow></msup><mo>⋅</mo><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msup><mrow><mn>3</mn></mrow><mrow><mn>23</mn></mrow></msup><mo>⋅</mo><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mspace></mspace><msup><mrow><mn>3</mn></mrow><mrow><mn>4371</mn></mrow></msup><mo>⋅</mo><mi>B</mi><mi>M</mi><mo>.</mo></math></span></span></span> This article focuses on the locally projective graph constructed by Giudici, Li and Praeger from the triality of the <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-geometry over <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>. We call it the <
{"title":"A characterisation of the triality locally projective graph","authors":"William Giuliano , Alexander A. Ivanov","doi":"10.1016/j.jalgebra.2024.11.033","DOIUrl":"10.1016/j.jalgebra.2024.11.033","url":null,"abstract":"<div><div>The paper contributes to the classification of locally projective graphs and their locally projective groups of automorphisms. This project aimed to merge sporadic and classical simple groups in a uniform setting. The list of known examples of locally projective groups of automorphisms includes the classical groups<span><span><span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mi>O</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mi>Ω</mi></mrow><mrow><mn>8</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo><mo>:</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>3</mn><mo>)</mo></math></span></span></span> as well as the sporadic simple groups<span><span><span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>22</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mn>23</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mn>24</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>H</mi><mi>e</mi><mo>,</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>J</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>B</mi><mi>M</mi><mo>,</mo><mspace></mspace><mi>M</mi><mo>,</mo></math></span></span></span> where <em>M</em> is the Monster sporadic simple group, the largest and most famous sporadic simple group. The locally projective graph for the Monster gives an important insight in the structure of 2-local subgroups in the Monster. The list also includes some remarkable non-split extensions which probably would not be discovered otherwise:<span><span><span><math><msup><mrow><mn>3</mn></mrow><mrow><mn>7</mn></mrow></msup><mo>⋅</mo><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>,</mo><mspace></mspace><msup><mrow><mn>3</mn></mrow><mrow><mn>23</mn></mrow></msup><mo>⋅</mo><mi>C</mi><msub><mrow><mi>o</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mspace></mspace><msup><mrow><mn>3</mn></mrow><mrow><mn>4371</mn></mrow></msup><mo>⋅</mo><mi>B</mi><mi>M</mi><mo>.</mo></math></span></span></span> This article focuses on the locally projective graph constructed by Giudici, Li and Praeger from the triality of the <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-geometry over <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>. We call it the <","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 305-324"},"PeriodicalIF":0.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-06DOI: 10.1016/j.jalgebra.2024.12.015
Austin Conner , Mateusz Michałek , Michael Schindler , Balázs Szendrői
We provide a description of a complete set of generators for the ideal that serves as the resultant ideal for n univariate polynomials of degree d. Our generators arise as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalizing the classical Sylvester resultant of two polynomials.
{"title":"Polynomial systems admitting a simultaneous solution","authors":"Austin Conner , Mateusz Michałek , Michael Schindler , Balázs Szendrői","doi":"10.1016/j.jalgebra.2024.12.015","DOIUrl":"10.1016/j.jalgebra.2024.12.015","url":null,"abstract":"<div><div>We provide a description of a complete set of generators for the ideal that serves as the resultant ideal for <em>n</em> univariate polynomials of degree <em>d</em>. Our generators arise as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalizing the classical Sylvester resultant of two polynomials.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 412-424"},"PeriodicalIF":0.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.jalgebra.2024.11.035
Humberto A. Diaz
We show that there are smooth projective surfaces X over a field F for which the cokernel of the extension of scalars map: is not of cofinite type.
{"title":"On the failure of Galois descent for Chow groups","authors":"Humberto A. Diaz","doi":"10.1016/j.jalgebra.2024.11.035","DOIUrl":"10.1016/j.jalgebra.2024.11.035","url":null,"abstract":"<div><div>We show that there are smooth projective surfaces <em>X</em> over a field <em>F</em> for which the cokernel of the extension of scalars map:<span><span><span><math><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>→</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mi>X</mi><msub><mrow><mo>×</mo></mrow><mrow><mi>F</mi></mrow></msub><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>)</mo></mrow><mrow><mi>G</mi><mi>a</mi><mi>l</mi><mo>(</mo><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>/</mo><mi>F</mi><mo>)</mo></mrow></msup></math></span></span></span> is not of cofinite type.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 203-210"},"PeriodicalIF":0.8,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.jalgebra.2024.11.032
Nicolas Guay, Peggy Jankovic, Mamoru Ueda
We extend to the super Yangian of the special linear Lie superalgebra and its affine version certain results related to Schur-Weyl duality. We do the same for the deformed double current superalgebra of , which is introduced here for the first time.
{"title":"Affine super Yangians and deformed double current superalgebras","authors":"Nicolas Guay, Peggy Jankovic, Mamoru Ueda","doi":"10.1016/j.jalgebra.2024.11.032","DOIUrl":"10.1016/j.jalgebra.2024.11.032","url":null,"abstract":"<div><div>We extend to the super Yangian of the special linear Lie superalgebra <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>m</mi><mo>|</mo><mi>n</mi></mrow></msub></math></span> and its affine version certain results related to Schur-Weyl duality. We do the same for the deformed double current superalgebra of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>m</mi><mo>|</mo><mi>n</mi></mrow></msub></math></span>, which is introduced here for the first time.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 598-652"},"PeriodicalIF":0.8,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143104846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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