Pub Date : 2025-12-08DOI: 10.1016/j.jalgebra.2025.12.007
Egle Bettio
Let be the number of distinct prime divisors occurring among the conjugacy class sizes of a finite group G, and let be the maximum number of such divisors in any single class size. We prove that the inequality holds for all finite groups, with no assumption of solvability. The bound is sharp, and refines earlier partial results.
{"title":"Huppert's ρ − σ conjecture for conjugacy class sizes","authors":"Egle Bettio","doi":"10.1016/j.jalgebra.2025.12.007","DOIUrl":"10.1016/j.jalgebra.2025.12.007","url":null,"abstract":"<div><div>Let <span><math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the number of distinct prime divisors occurring among the conjugacy class sizes of a finite group <em>G</em>, and let <span><math><mi>σ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the maximum number of such divisors in any single class size. We prove that the inequality <span><math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>3</mn><mi>σ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>1</mn></math></span> holds for all finite groups, with no assumption of solvability. The bound is sharp, and refines earlier partial results.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 518-525"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733658","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 : 2025-12-08DOI: 10.1016/j.jalgebra.2025.12.006
Victor Guba
A (discrete) group is called amenable if there exists a finitely additive right-invariant probability measure on it. The question of whether Thompson's group F is amenable is a long-standing open problem. We consider the presentation of F in terms of non-spherical semigroup diagrams. There is a natural partition of F into 7 parts in terms of these diagrams. We show that for any finitely additive right-invariant probability measure on F, all but one of these sets have zero measure. This helps to clarify the structure of Følner sets in F, provided the group is amenable.
{"title":"On zero-measured subsets of Thompson's group F","authors":"Victor Guba","doi":"10.1016/j.jalgebra.2025.12.006","DOIUrl":"10.1016/j.jalgebra.2025.12.006","url":null,"abstract":"<div><div>A (discrete) group is called <em>amenable</em> if there exists a finitely additive right-invariant probability measure on it. The question of whether Thompson's group <em>F</em> is amenable is a long-standing open problem. We consider the presentation of <em>F</em> in terms of non-spherical semigroup diagrams. There is a natural partition of <em>F</em> into 7 parts in terms of these diagrams. We show that for any finitely additive right-invariant probability measure on <em>F</em>, all but one of these sets have zero measure. This helps to clarify the structure of Følner sets in <em>F</em>, provided the group is amenable.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 106-122"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145750307","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 : 2025-12-08DOI: 10.1016/j.jalgebra.2025.12.001
Shengkai Mao
Let be an isogeny between linear algebraic groups over a number field E, S be a finite set of places of E. In this note, we give some criteria for when a S-congruence subgroup of has S-congruence image in following [7].
{"title":"Isogenies and congruence subgroups","authors":"Shengkai Mao","doi":"10.1016/j.jalgebra.2025.12.001","DOIUrl":"10.1016/j.jalgebra.2025.12.001","url":null,"abstract":"<div><div>Let <span><math><mi>π</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span> be an isogeny between linear algebraic groups over a number field <em>E</em>, <em>S</em> be a finite set of places of <em>E</em>. In this note, we give some criteria for when a <em>S</em>-congruence subgroup of <span><math><mi>G</mi><mo>(</mo><mi>E</mi><mo>)</mo></math></span> has <em>S</em>-congruence image in <span><math><mi>H</mi><mo>(</mo><mi>E</mi><mo>)</mo></math></span> following <span><span>[7]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 781-810"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733716","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 : 2025-12-08DOI: 10.1016/j.jalgebra.2025.11.030
Vera Serganova , Arkady Vaintrob
An almost inner derivation of a Lie algebra L is a derivation that coincides with an inner derivation on each one-dimensional subspace of L. The almost inner derivations form a subalgebra of the Lie algebra of all derivations of L, containing the inner derivations as an ideal. If L is a simple finite-dimensional Lie algebra, then , since all derivations of L are inner.
In this paper, we introduce and study almost inner derivations of Lie superalgebras. Since simple Lie superalgebras may admit non-inner outer derivations, the existence of non-inner almost inner derivations becomes a nontrivial question. Nevertheless, we show that all almost inner derivations of finite-dimensional simple Lie superalgebras over are inner. We also give examples of naturally occurring non-inner almost inner derivations of some quasireductive Lie superalgebras related to the Sato-Kimura classification of prehomogeneous vector spaces.
{"title":"Almost inner derivations of Lie superalgebras","authors":"Vera Serganova , Arkady Vaintrob","doi":"10.1016/j.jalgebra.2025.11.030","DOIUrl":"10.1016/j.jalgebra.2025.11.030","url":null,"abstract":"<div><div>An almost inner derivation of a Lie algebra <em>L</em> is a derivation that coincides with an inner derivation on each one-dimensional subspace of <em>L</em>. The almost inner derivations form a subalgebra <span><math><mi>aDer</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span> of the Lie algebra <span><math><mi>Der</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span> of all derivations of <em>L</em>, containing the inner derivations <span><math><mi>iDer</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span> as an ideal. If <em>L</em> is a simple finite-dimensional Lie algebra, then <span><math><mi>aDer</mi><mo>(</mo><mi>L</mi><mo>)</mo><mo>=</mo><mi>iDer</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span>, since all derivations of <em>L</em> are inner.</div><div>In this paper, we introduce and study almost inner derivations of Lie superalgebras. Since simple Lie superalgebras may admit non-inner outer derivations, the existence of non-inner almost inner derivations becomes a nontrivial question. Nevertheless, we show that all almost inner derivations of finite-dimensional simple Lie superalgebras over <span><math><mi>C</mi></math></span> are inner. We also give examples of naturally occurring non-inner almost inner derivations of some quasireductive Lie superalgebras related to the Sato-Kimura classification of prehomogeneous vector spaces.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 1-26"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145718953","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 : 2025-12-08DOI: 10.1016/j.jalgebra.2025.12.003
Emiliano Liwski , Fatemeh Mohammadi , Rémi Prébet
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal dependencies, which play a central role in modeling determinantal varieties, rigidity problems, and conditional independence relations. We introduce an efficient computational strategy for decomposing the circuit variety of a given matroid M, based on an algorithm that identifies its maximal degenerations. These degenerations correspond to the largest matroids lying below M in the weak order. Our framework yields explicit and computable decompositions of circuit varieties that were previously out of reach for symbolic or numerical algebra systems. We apply our strategy to several classical configurations, including the Vámos matroid, the unique Steiner quadruple system , projective and affine planes, the dual of the Fano matroid, and the dual of the graphic matroid of . In each case, we successfully compute the minimal irreducible decomposition of their circuit varieties.
{"title":"Efficient algorithms for maximal matroid degenerations and irreducible decompositions of circuit varieties","authors":"Emiliano Liwski , Fatemeh Mohammadi , Rémi Prébet","doi":"10.1016/j.jalgebra.2025.12.003","DOIUrl":"10.1016/j.jalgebra.2025.12.003","url":null,"abstract":"<div><div>Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal dependencies, which play a central role in modeling determinantal varieties, rigidity problems, and conditional independence relations. We introduce an efficient computational strategy for decomposing the circuit variety of a given matroid <em>M</em>, based on an algorithm that identifies its maximal degenerations. These degenerations correspond to the largest matroids lying below <em>M</em> in the weak order. Our framework yields explicit and computable decompositions of circuit varieties that were previously out of reach for symbolic or numerical algebra systems. We apply our strategy to several classical configurations, including the Vámos matroid, the unique Steiner quadruple system <span><math><mi>S</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></span>, projective and affine planes, the dual of the Fano matroid, and the dual of the graphic matroid of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></math></span>. In each case, we successfully compute the minimal irreducible decomposition of their circuit varieties.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 526-576"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733652","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 : 2025-12-05DOI: 10.1016/j.jalgebra.2025.11.029
Jadyn V. Breland, Sam K. Miller
We define the notion of a Brauer pair of a chain complex, extending the notion of a Brauer pair of a p-permutation module introduced by Boltje and Perepelitsky. In fact, the Brauer pairs of a splendid Rickard equivalence C coincide with the set of Brauer pairs of the corresponding p-permutation equivalence induced by C. As a result, we derive structural results for splendid Rickard equivalences that correspond to known structural properties for p-permutation equivalences. In particular, we show splendid Rickard equivalences induce local splendid Rickard equivalences between normalizer block algebras as well as centralizer block algebras.
{"title":"Brauer pairs for splendid Rickard equivalences","authors":"Jadyn V. Breland, Sam K. Miller","doi":"10.1016/j.jalgebra.2025.11.029","DOIUrl":"10.1016/j.jalgebra.2025.11.029","url":null,"abstract":"<div><div>We define the notion of a Brauer pair of a chain complex, extending the notion of a Brauer pair of a <em>p</em>-permutation module introduced by Boltje and Perepelitsky. In fact, the Brauer pairs of a splendid Rickard equivalence <em>C</em> coincide with the set of Brauer pairs of the corresponding <em>p</em>-permutation equivalence <span><math><mi>Λ</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></span> induced by <em>C</em>. As a result, we derive structural results for splendid Rickard equivalences that correspond to known structural properties for <em>p</em>-permutation equivalences. In particular, we show splendid Rickard equivalences induce local splendid Rickard equivalences between normalizer block algebras as well as centralizer block algebras.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 694-729"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733654","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 : 2025-12-05DOI: 10.1016/j.jalgebra.2025.11.028
Darlayne Addabbo , Christoph A. Keller
It is known from Zhu's results that under modular transformations, correlators of rational -cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that have zero modes inserted. We derive recursion relations for such correlators and use them to establish modular transformation properties. For holomorphic VOAs we find that correlators with only zero modes transform like quasi-modular forms, and mixed correlators with both zero modes and vertex operators transform like quasi-Jacobi forms. As an application of our results, we introduce algebras of higher weight fields whose zero mode correlators mimic the properties of those of weight 1 fields. We also give a simplified proof of the weight 1 transformation properties originally proven by Miyamoto.
{"title":"Modularity of vertex operator algebra correlators with zero modes","authors":"Darlayne Addabbo , Christoph A. Keller","doi":"10.1016/j.jalgebra.2025.11.028","DOIUrl":"10.1016/j.jalgebra.2025.11.028","url":null,"abstract":"<div><div>It is known from Zhu's results that under modular transformations, correlators of rational <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that have zero modes inserted. We derive recursion relations for such correlators and use them to establish modular transformation properties. For holomorphic VOAs we find that correlators with only zero modes transform like quasi-modular forms, and mixed correlators with both zero modes and vertex operators transform like quasi-Jacobi forms. As an application of our results, we introduce algebras of higher weight fields whose zero mode correlators mimic the properties of those of weight 1 fields. We also give a simplified proof of the weight 1 transformation properties originally proven by Miyamoto.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 27-69"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145750306","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 : 2025-12-05DOI: 10.1016/j.jalgebra.2025.11.031
Ruipeng Zhu
This paper shows that if H is a Hopf algebra and is a faithfully flat H-Galois extension, then B is skew Calabi–Yau provided A and H are. Specifically, for cleft extensions , the Nakayama automorphism of B can be derived from those of A and H, along with the homological determinant of the H-action on A. This finding is based on the study of the Hopf bimodule structure on .
{"title":"Skew Calabi–Yau property of faithfully flat Hopf Galois extensions","authors":"Ruipeng Zhu","doi":"10.1016/j.jalgebra.2025.11.031","DOIUrl":"10.1016/j.jalgebra.2025.11.031","url":null,"abstract":"<div><div>This paper shows that if <em>H</em> is a Hopf algebra and <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span> is a faithfully flat <em>H</em>-Galois extension, then <em>B</em> is skew Calabi–Yau provided <em>A</em> and <em>H</em> are. Specifically, for cleft extensions <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span>, the Nakayama automorphism of <em>B</em> can be derived from those of <em>A</em> and <em>H</em>, along with the homological determinant of the <em>H</em>-action on <em>A</em>. This finding is based on the study of the Hopf bimodule structure on <span><math><msubsup><mrow><mi>Ext</mi></mrow><mrow><msup><mrow><mi>A</mi></mrow><mrow><mi>e</mi></mrow></msup></mrow><mrow><mi>i</mi></mrow></msubsup><mo>(</mo><mi>A</mi><mo>,</mo><msup><mrow><mi>B</mi></mrow><mrow><mi>e</mi></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 597-647"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733656","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 : 2025-12-05DOI: 10.1016/j.jalgebra.2025.11.019
Dmitriy Voloshyn
We study the decomposition of a generic element of a connected reductive complex algebraic group G in the form where and are rational maps onto a unipotent subgroup and a Borel subgroup opposite to , and is a representative of a Weyl group element u. We introduce a class of rational Weyl group elements that give rise to such decompositions, and study their various properties.
{"title":"Multiple rational normal forms in Lie theory","authors":"Dmitriy Voloshyn","doi":"10.1016/j.jalgebra.2025.11.019","DOIUrl":"10.1016/j.jalgebra.2025.11.019","url":null,"abstract":"<div><div>We study the decomposition of a generic element <span><math><mi>g</mi><mo>∈</mo><mi>G</mi></math></span> of a connected reductive complex algebraic group <em>G</em> in the form <span><math><mi>g</mi><mo>=</mo><mi>N</mi><mo>(</mo><mi>g</mi><mo>)</mo><mi>B</mi><mo>(</mo><mi>g</mi><mo>)</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>N</mi><msup><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> where <span><math><mi>N</mi><mo>:</mo><mi>G</mi><mo>⇢</mo><msub><mrow><mi>N</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> and <span><math><mi>B</mi><mo>:</mo><mi>G</mi><mo>⇢</mo><msub><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> are rational maps onto a unipotent subgroup <span><math><msub><mrow><mi>N</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> and a Borel subgroup <span><math><msub><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> opposite to <span><math><msub><mrow><mi>N</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, and <span><math><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> is a representative of a Weyl group element <em>u</em>. We introduce a class of rational Weyl group elements that give rise to such decompositions, and study their various properties.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 453-487"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733660","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 : 2025-12-05DOI: 10.1016/j.jalgebra.2025.11.032
Clara Franchi , Mario Mainardis
We use Majorana representations to study the subalgebras of the Griess algebra that have shape and whose associated Miyamoto groups are isomorphic to . We prove that these subalgebras exist only if . The case was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case we prove that these algebras are all isomorphic and provide their precise description. In case we prove that these algebras do not arise from standard Majorana representations.
{"title":"On subalgebras of the Griess algebra with alternating Miyamoto group","authors":"Clara Franchi , Mario Mainardis","doi":"10.1016/j.jalgebra.2025.11.032","DOIUrl":"10.1016/j.jalgebra.2025.11.032","url":null,"abstract":"<div><div>We use Majorana representations to study the subalgebras of the Griess algebra that have shape <span><math><mo>(</mo><mn>2</mn><mi>B</mi><mo>,</mo><mn>3</mn><mi>A</mi><mo>,</mo><mn>5</mn><mi>A</mi><mo>)</mo></math></span> and whose associated Miyamoto groups are isomorphic to <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We prove that these subalgebras exist only if <span><math><mi>n</mi><mo>∈</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>}</mo></math></span>. The case <span><math><mi>n</mi><mo>=</mo><mn>5</mn></math></span> was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case <span><math><mi>n</mi><mo>=</mo><mn>6</mn></math></span> we prove that these algebras are all isomorphic and provide their precise description. In case <span><math><mi>n</mi><mo>=</mo><mn>8</mn></math></span> we prove that these algebras do not arise from standard Majorana representations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"691 ","pages":"Pages 811-854"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733717","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号