Journal of Algebra最新文献

英文中文

Modules induced from large subalgebras of the Lie algebra of differential operators of degree at most one

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2025.01.008

Matthew Ondrus

We study the representation theory of the Lie algebra

D

of differential operators of degree at most one on the algebra of complex Laurent polynomials. We define a natural family of subalgebras of

D

, which we call polynomial subalgebras. After classifying the one-dimensional modules for polynomial subalgebras, we use these one-dimensional modules to construct corresponding induced modules for the full Lie algebra

D

. These induced modules are frequently simple and generalize a family of recently discovered simple modules. In order to understand these induced modules in certain complicated cases, we take advantage of some general results on tensor products of modules.

引用次数: 0

A combinatorial generalisation of rank two complex reflection groups via generators and relations

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2024.12.032

Igor Haladjian

Complex reflection groups of rank two are precisely the finite groups in the family of groups that we call J-reflection groups. These groups are particular cases of J-groups as defined by Achar & Aubert in 2008. The family of J-reflection groups generalise both complex reflection groups of rank two and toric reflection groups, a family of groups defined and studied by Gobet. We give uniform presentations by generators and relations of J-reflection groups, which coincide with the presentations given by Broué, Malle and Rouquier when the groups are finite. In particular, these presentations provide uniform presentations for complex reflection groups of rank two where the generators are reflections (however the proof uses the classification of irreducible complex reflection groups). Moreover, we show that the center of J-reflection groups is cyclic, generalising what happens for irreducible complex reflection groups of rank two and toric reflection groups. Finally, we classify J-reflection groups up to reflection isomorphisms.

引用次数: 0

Computing supersingular endomorphism rings using inseparable endomorphisms

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2025.01.012

Jenny Fuselier , Annamaria Iezzi , Mark Kozek , Travis Morrison , Changningphaabi Namoijam

We give an algorithm for computing an inseparable endomorphism of a supersingular elliptic curve E defined over

F_{p^{2}}

, which, conditional on GRH, runs in expected

O (p^{1 / 2} {(\log p)}^{2} {(\log \log p)}^{3})

bit operations and requires

O ({(\log p)}^{2})

storage. This matches the time and storage complexity of the best conditional algorithms for computing a nontrivial supersingular endomorphism, such as those of Eisenträger–Hallgren–Leonardi–Morrison–Park and Delfs–Galbraith. Unlike these prior algorithms, which require two paths from E to a curve defined over

F_{p}

, the algorithm we introduce only requires one; thus when combined with the algorithm of Corte-Real Santos–Costello–Shi, our algorithm will be faster in practice. Moreover, our algorithm produces endomorphisms with predictable discriminants, enabling us to prove properties about the orders they generate. With two calls to our algorithm, we can provably compute a Bass suborder of

End (E)

. This result is then used in an algorithm for computing a basis for

End (E)

with the same time complexity, assuming GRH. We also argue that

End (E)

can be computed using

O (1)

calls to our algorithm along with polynomial overhead, conditional on a heuristic assumption about the distribution of the discriminants of these endomorphisms. Conditional on GRH and this additional heuristic, this yields a

O (p^{1 / 2} {(\log p)}^{2} {(\log \log p)}^{3})

algorithm for computing

End (E)

requiring

O ({(\log p)}^{2})

storage.

{"title":"Computing supersingular endomorphism rings using inseparable endomorphisms","authors":"Jenny Fuselier , Annamaria Iezzi , Mark Kozek , Travis Morrison , Changningphaabi Namoijam","doi":"10.1016/j.jalgebra.2025.01.012","DOIUrl":"10.1016/j.jalgebra.2025.01.012","url":null,"abstract":"<div><div>We give an algorithm for computing an inseparable endomorphism of a supersingular elliptic curve E defined over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math>, which, conditional on GRH, runs in expected <math><mi>O</mi><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> bit operations and requires <math><mi>O</mi><mo>(</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> storage. This matches the time and storage complexity of the best conditional algorithms for computing a nontrivial supersingular endomorphism, such as those of Eisenträger–Hallgren–Leonardi–Morrison–Park and Delfs–Galbraith. Unlike these prior algorithms, which require two paths from E to a curve defined over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, the algorithm we introduce only requires one; thus when combined with the algorithm of Corte-Real Santos–Costello–Shi, our algorithm will be faster in practice. Moreover, our algorithm produces endomorphisms with predictable discriminants, enabling us to prove properties about the orders they generate. With two calls to our algorithm, we can provably compute a Bass suborder of <math><mi>End</mi><mo>(</mo><mi>E</mi><mo>)</mo></math>. This result is then used in an algorithm for computing a basis for <math><mi>End</mi><mo>(</mo><mi>E</mi><mo>)</mo></math> with the same time complexity, assuming GRH. We also argue that <math><mi>End</mi><mo>(</mo><mi>E</mi><mo>)</mo></math> can be computed using <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> calls to our algorithm along with polynomial overhead, conditional on a heuristic assumption about the distribution of the discriminants of these endomorphisms. Conditional on GRH and this additional heuristic, this yields a <math><mi>O</mi><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> algorithm for computing <math><mi>End</mi><mo>(</mo><mi>E</mi><mo>)</mo></math> requiring <math><mi>O</mi><mo>(</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>p</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> storage.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"668 ","pages":"Pages 145-189"},"PeriodicalIF":0.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163260","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}

引用次数: 0

AI-rings on almost completely decomposable Abelian groups

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2025.01.007

Ekaterina Kompantseva , Askar Tuganbaev

We consider the class

A_{0}

of reduced abelian block-rigid CRQ-groups of ring type. An absolute ideal of an abelian group G is a subgroup of G which is an ideal in any ring on G. A ring R is called an AI-ring if any ideal of R is an absolute ideal of its additive group. An abelian group G is called an RAI-group if there exists at least one AI-ring on G. It is proved that any group in

A_{0}

is an RAI-group. Thus, in the class

A_{0}

, we solve Problem 93 in the monograph Fuchs (1973) [9]. We classify AI-rings on groups in the class

A_{0}

引用次数: 0

Generalized Verma modules induced from infinite dimensional simple Uq(sl2)-modules

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2024.12.035

Limeng Xia

Let

g

be a simple complex finite dimensional Lie algebra. For generic

q \in C^{⁎}

, let

U_{q} (g)

be the quantum group with standard generators

E_{i}, F_{i}, q^{\pm λ_{i}}

. Fixing an index

i_{0}

, let

P

be the subalgebra generated by all

E_{i}, q^{\pm λ_{i}}

and

F_{i_{0}}

, which has sub-quotient algebras isomorphic to

U_{q_{i_{0}}} ({sl}_{2})

. With each generalized Verma

U_{q} (g)

-module

M_{P} (V)

induced from a simple

U_{q_{i_{0}}} ({sl}_{2})

-module V, we associate a Verma module

M (V)

. In this paper, for infinite dimensional V we prove that

M_{P} (V)

is simple if and only if

M (V)

is simple.

引用次数: 0

Codimensions of algebras with pseudoautomorphism and their exponential growth

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-23 DOI: 10.1016/j.jalgebra.2025.01.015

Elena Campedel, Ginevra Giordani, Antonio Ioppolo

Let F be a fixed field of characteristic zero containing an element i such that

i^{2} = - 1

. In this paper we consider finite dimensional superalgebras over F endowed with a pseudoautomorphism p and we investigate the asymptotic behavior of the corresponding sequence of p-codimensions

c_{n}^{p} (A)

n = 1, 2, \dots

. First we give a positive answer to a conjecture of Amitsur in this setting: the p-exponent

\exp^{p} (A) = \lim_{n \to \infty} \sqrt[n]{c_{n}^{p} (A)}

always exists and it is an integer. In the final part we characterize the algebras whose exponential growth is bounded by 2.

引用次数: 0

Characters and Sylow subgroup abelianization

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-22 DOI: 10.1016/j.jalgebra.2024.12.031

Eugenio Giannelli , Noelia Rizo , A.A. Schaeffer Fry , Carolina Vallejo

We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect.

引用次数: 0

Lefschetz properties of squarefree monomial ideals via Rees algebras

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-22 DOI: 10.1016/j.jalgebra.2024.12.030

Thiago Holleben

The theory of Rees algebras of monomial ideals has been extensively studied, and as a consequence, many (sometimes partial) equivalences between algebraic properties of monomial ideals, and combinatorial properties of simplicial complexes and hypergraphs are known. In this paper we show how this theory can be used to find interesting examples in the theory of Lefschetz properties. We explore the consequences of known results from Lefschetz properties for the Rees algebras of squarefree monomial ideals, for example in the calculation of analytic spread. In particular, we show a connection between symbolic powers and f-vectors of simplicial complexes. This perspective leads us to a generalization of Postnikov's “mixed Eulerian numbers”. We prove the positivity of such numbers in our setting.

引用次数: 0

Coincidences between intervals in two partial orders on complex reflection groups

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-22 DOI: 10.1016/j.jalgebra.2024.12.034

Joel Brewster Lewis , Jiayuan Wang

In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order structure called the absolute order. In complex reflection groups, the reflection length is no longer always equal to the codimension of fixed space, and the two functions give rise to two different partial orders on the group. We characterize the elements w in the combinatorial family

G (m, p, n)

of complex reflection groups for which the intervals below w in these two posets coincide. We also explore the relationship between this property and other natural properties of elements in complex reflection groups; some general theory of posets arising from subadditive functions on groups; and the particular case of subadditive functions on the symmetric group.

引用次数: 0

Variations on the Thompson theorem

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-21 DOI: 10.1016/j.jalgebra.2024.12.029

Hung P. Tong-Viet

Thompson's theorem states that a finite group G is solvable if and only if every 2-generated subgroup of G is solvable. In this paper, we prove some new criteria for both solvability and nilpotency of a finite group using certain conditions on 2-generated subgroups. We show that a finite group G is solvable if and only if for every pair of two elements x and y in G of coprime prime power order, if

〈 x, y 〉

is solvable, then

〈 x, y^{g} 〉

is solvable for all

g \in G

. Similarly, a finite group G is nilpotent if and only if for every pair of elements x and y in G of coprime prime power order, if

〈 x, y 〉

is solvable, then x and

y^{g}

commute for some

g \in G

. Some applications to graphs defined on groups are given.

{"title":"Variations on the Thompson theorem","authors":"Hung P. Tong-Viet","doi":"10.1016/j.jalgebra.2024.12.029","DOIUrl":"10.1016/j.jalgebra.2024.12.029","url":null,"abstract":"<div><div>Thompson's theorem states that a finite group G is solvable if and only if every 2-generated subgroup of G is solvable. In this paper, we prove some new criteria for both solvability and nilpotency of a finite group using certain conditions on 2-generated subgroups. We show that a finite group G is solvable if and only if for every pair of two elements x and y in G of coprime prime power order, if <math><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></math> is solvable, then <math><mo>〈</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>g</mi></mrow></msup><mo>〉</mo></math> is solvable for all <math><mi>g</mi><mo>∈</mo><mi>G</mi></math>. Similarly, a finite group G is nilpotent if and only if for every pair of elements x and y in G of coprime prime power order, if <math><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></math> is solvable, then x and <math><msup><mrow><mi>y</mi></mrow><mrow><mi>g</mi></mrow></msup></math> commute for some <math><mi>g</mi><mo>∈</mo><mi>G</mi></math>. Some applications to graphs defined on groups are given.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"668 ","pages":"Pages 46-74"},"PeriodicalIF":0.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164150","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}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Algebra

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀