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Primitive divisors of Lucas sequences in polynomial rings
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-12 DOI: 10.1016/j.jalgebra.2025.03.008
Joaquim Cera Da Conceição
{"title":"Primitive divisors of Lucas sequences in polynomial rings","authors":"Joaquim Cera Da Conceição","doi":"10.1016/j.jalgebra.2025.03.008","DOIUrl":"10.1016/j.jalgebra.2025.03.008","url":null,"abstract":"<div><div>It is known that all terms <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of a classical regular Lucas sequence have a primitive prime divisor if <span><math><mi>n</mi><mo>&gt;</mo><mn>30</mn></math></span> <span><span>[2]</span></span>. In addition, a complete description of all regular Lucas sequences and their terms <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><mn>2</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>30</mn></math></span>, which do not have a primitive divisor is also known. Here, we prove comparable results for Lucas sequences in polynomial rings, correcting some previous theorem on the same subject. The first part of our paper develops some elements of Lucas theory in several abstract settings before proving our main theorem in polynomial rings.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"672 ","pages":"Pages 400-412"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642281","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
Stiefel-Whitney Classes for finite special linear groups of even rank
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-12 DOI: 10.1016/j.jalgebra.2025.03.009
Neha Malik , Steven Spallone
{"title":"Stiefel-Whitney Classes for finite special linear groups of even rank","authors":"Neha Malik ,&nbsp;Steven Spallone","doi":"10.1016/j.jalgebra.2025.03.009","DOIUrl":"10.1016/j.jalgebra.2025.03.009","url":null,"abstract":"<div><div>We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal representations of special linear groups <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> when <em>n</em> and <em>q</em> are odd. These classes are expressed in terms of character values at diagonal elements of order 2. We give several consequences, and work out the 4th SWC explicitly, and the 8th SWC when the 4th vanishes.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"673 ","pages":"Pages 455-473"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636425","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
Quantum super-spherical pairs
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-12 DOI: 10.1016/j.jalgebra.2025.03.010
D. Algethami , A. Mudrov , V. Stukopin
{"title":"Quantum super-spherical pairs","authors":"D. Algethami ,&nbsp;A. Mudrov ,&nbsp;V. Stukopin","doi":"10.1016/j.jalgebra.2025.03.010","DOIUrl":"10.1016/j.jalgebra.2025.03.010","url":null,"abstract":"<div><div>We introduce quantum super-spherical pairs as coideal subalgebras in general linear and orthosymplectic quantum supergroups. These subalgebras play a role of isotropy subgroups for matrices solving the <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-graded reflection equation. They generalize quantum (pseudo)-symmetric pairs of Letzter-Kolb-Regelskis-Vlaar.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 276-313"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685270","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
Conjugation on reddening sequences and conjugation difference
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-12 DOI: 10.1016/j.jalgebra.2025.03.003
Siyang Liu , Jie Pan
{"title":"Conjugation on reddening sequences and conjugation difference","authors":"Siyang Liu ,&nbsp;Jie Pan","doi":"10.1016/j.jalgebra.2025.03.003","DOIUrl":"10.1016/j.jalgebra.2025.03.003","url":null,"abstract":"<div><div>We describe the conjugation of the reddening sequence according to the formula of <em>c</em>-vectors with respect to changing the initial seed. As applications, we extend the Rotation Lemma, the Target before Source Theorem, and the mutation invariant property of the existence of reddening sequences to totally sign-skew-symmetric cluster algebras. Furthermore, this also leads to the construction of conjugation difference which characterizes the number of red mutations a maximal green sequence should admit in any matrix pattern with the initial seed changed via mutations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"671 ","pages":"Pages 95-116"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644115","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
Straightening laws for Chow rings of matroids
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-10 DOI: 10.1016/j.jalgebra.2025.02.033
Matt Larson
{"title":"Straightening laws for Chow rings of matroids","authors":"Matt Larson","doi":"10.1016/j.jalgebra.2025.02.033","DOIUrl":"10.1016/j.jalgebra.2025.02.033","url":null,"abstract":"<div><div>We give elementary and non-inductive proofs of three fundamental theorems about Chow rings of matroids: the standard monomial basis, Poincaré duality, and the dragon-Hall–Rado formula. Our approach, which also works for augmented Chow rings of matroids, is based on a straightening law. This approach gives a decomposition of the Chow ring of a matroid into pieces indexed by flats.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"672 ","pages":"Pages 50-70"},"PeriodicalIF":0.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600950","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
Representations over diagrams of abelian categories I: Global structure and homological objects
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-10 DOI: 10.1016/j.jalgebra.2025.01.033
Zhenxing Di , Liping Li , Li Liang , Nina Yu
{"title":"Representations over diagrams of abelian categories I: Global structure and homological objects","authors":"Zhenxing Di ,&nbsp;Liping Li ,&nbsp;Li Liang ,&nbsp;Nina Yu","doi":"10.1016/j.jalgebra.2025.01.033","DOIUrl":"10.1016/j.jalgebra.2025.01.033","url":null,"abstract":"<div><div>Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations between them, and characterize special homological objects. These results lay a foundation for our future works.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"672 ","pages":"Pages 208-246"},"PeriodicalIF":0.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619641","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
Rose–Terao–Yuzvinsky theorem for reduced forms
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-07 DOI: 10.1016/j.jalgebra.2025.02.022
Ricardo Burity , Zaqueu Ramos , Aron Simis , Ştefan O. Tohǎneanu
{"title":"Rose–Terao–Yuzvinsky theorem for reduced forms","authors":"Ricardo Burity ,&nbsp;Zaqueu Ramos ,&nbsp;Aron Simis ,&nbsp;Ştefan O. Tohǎneanu","doi":"10.1016/j.jalgebra.2025.02.022","DOIUrl":"10.1016/j.jalgebra.2025.02.022","url":null,"abstract":"<div><div>Yuzvinsky and Rose–Terao have shown that the homological dimension of the gradient ideal of the defining polynomial of a generic hyperplane arrangement is maximum possible. In this work one provides yet another proof of this result, which in addition is totally different from the one given by Burity–Simis–Tohǎneanu in a previous work. Another main drive of the paper concerns a version of the above result in the case of a product of general forms of arbitrary degrees (in particular, transverse ones). Finally, some relevant cases of non general forms are also contemplated.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"673 ","pages":"Pages 45-76"},"PeriodicalIF":0.8,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620733","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
Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-06 DOI: 10.1016/j.jalgebra.2025.01.032
Yuki Kanakubo
{"title":"Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras","authors":"Yuki Kanakubo","doi":"10.1016/j.jalgebra.2025.01.032","DOIUrl":"10.1016/j.jalgebra.2025.01.032","url":null,"abstract":"<div><div>For a Kac-Moody algebra <span><math><mi>g</mi></math></span> of rank 2 and a fundamental weight <em>λ</em>, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths <span><math><mi>B</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span> and monomial realization <span><math><mi>M</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span>. As an application, we also give an explicit form of monomial realization <span><math><mi>M</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span> in terms of Weyl groups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"672 ","pages":"Pages 31-49"},"PeriodicalIF":0.8,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577124","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
Symplectic Leibniz algebras as a non-commutative version of symplectic Lie algebras
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-06 DOI: 10.1016/j.jalgebra.2025.03.001
Fatima-Ezzahrae Abid, Mohamed Boucetta
{"title":"Symplectic Leibniz algebras as a non-commutative version of symplectic Lie algebras","authors":"Fatima-Ezzahrae Abid,&nbsp;Mohamed Boucetta","doi":"10.1016/j.jalgebra.2025.03.001","DOIUrl":"10.1016/j.jalgebra.2025.03.001","url":null,"abstract":"<div><div>We introduce symplectic left Leibniz algebras and symplectic right Leibniz algebras as generalizations of symplectic Lie algebras. These algebras possess a left symmetric product and are Lie-admissible. We describe completely symmetric Leibniz algebras that are symplectic as both left and right Leibniz algebras. Additionally, we show that symplectic left or right Leibniz algebras can be constructed from a symplectic Lie algebra and a vector space through a method that combines the double extension process and the <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extension. This approach allows us to generate a broad class of examples.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"673 ","pages":"Pages 1-35"},"PeriodicalIF":0.8,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600494","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
Local isomorphism classes of fractional ideals of orders in étale algebras
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-03-06 DOI: 10.1016/j.jalgebra.2025.02.030
Stefano Marseglia
{"title":"Local isomorphism classes of fractional ideals of orders in étale algebras","authors":"Stefano Marseglia","doi":"10.1016/j.jalgebra.2025.02.030","DOIUrl":"10.1016/j.jalgebra.2025.02.030","url":null,"abstract":"<div><div>We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"673 ","pages":"Pages 77-102"},"PeriodicalIF":0.8,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619326","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}
引用次数: 0
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