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Representation theory of very non-standard quantum so(2N−1) 非标准量子so（2N−1）的表示理论
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-08 DOI: 10.1016/j.jpaa.2025.107990
Stefan Kolb, Jake Stephens
{"title":"Representation theory of very non-standard quantum so(2N−1)","authors":"Stefan Kolb,&nbsp;Jake Stephens","doi":"10.1016/j.jpaa.2025.107990","DOIUrl":"10.1016/j.jpaa.2025.107990","url":null,"abstract":"<div><div>We classify the finite dimensional representations of the quantum symmetric pair coideal subalgebra <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> of type <em>DII</em> corresponding to the symmetric pair <span><math><mo>(</mo><mrow><mi>so</mi></mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo><mo>,</mo><mrow><mi>so</mi></mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>. For <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> defined over an arbitrary field <em>k</em> and <span><math><mi>q</mi><mo>∈</mo><mi>k</mi><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span> not a root of unity we establish a one-to-one correspondence between finite dimensional, simple <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>-modules and dominant integral weights for <span><math><mrow><mi>so</mi></mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. We use specialisation to show that the category of finite dimensional <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>-modules is semisimple if <span><math><mrow><mi>char</mi></mrow><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> and <em>q</em> is transcendental over <span><math><mi>Q</mi></math></span>. In this case the characters of simple <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>-modules are given by Weyl's character formula. This means in particular that the quantum symmetric pair of type <em>DII</em> can be used to obtain Gelfand-Tsetlin bases for irreducible representations of the Drinfeld-Jimbo quantum group <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mrow><mi>so</mi></mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107990"},"PeriodicalIF":0.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143946556","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
Generalised spherical minors and their relations 广义球面小调及其关系
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-08 DOI: 10.1016/j.jpaa.2025.107989
Luca Francone
{"title":"Generalised spherical minors and their relations","authors":"Luca Francone","doi":"10.1016/j.jpaa.2025.107989","DOIUrl":"10.1016/j.jpaa.2025.107989","url":null,"abstract":"<div><div>Let <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group <em>G</em>. We define some functions on the homogeneous space <span><math><mi>G</mi><mo>/</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> that we call <em>generalised spherical minors</em>. When <span><math><mi>G</mi><mo>=</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>×</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>, we recover Fomin-Zelevinsky generalised minors. We prove that generalised spherical minors satisfy some integer coefficients polynomial relations, that extend <span><span>[9, Theorem 1.17]</span></span> and that have the shape of exchange relations of LP-algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107989"},"PeriodicalIF":0.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947140","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
Corrigendum to “Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras” [J. Pure Appl. Algebra 227(4) (2023) 107281] “切环Hecke代数和切环Schur代数的中心上的迹形”的更正[J]。纯粹的达成。代数227(4)(2023)107281]
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-05-02 DOI: 10.1016/j.jpaa.2025.107981
Zhekun He , Jun Hu , Huang Lin
{"title":"Corrigendum to “Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras” [J. Pure Appl. Algebra 227(4) (2023) 107281]","authors":"Zhekun He ,&nbsp;Jun Hu ,&nbsp;Huang Lin","doi":"10.1016/j.jpaa.2025.107981","DOIUrl":"10.1016/j.jpaa.2025.107981","url":null,"abstract":"","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107981"},"PeriodicalIF":0.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895031","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
Le théorème de Lüroth pour les corps de fractions tordus par un automorphisme fini 由有限自同构弯曲的分数场的Luroth定理
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-28 DOI: 10.1016/j.jpaa.2025.107982
Bruno Deschamps
{"title":"Le théorème de Lüroth pour les corps de fractions tordus par un automorphisme fini","authors":"Bruno Deschamps","doi":"10.1016/j.jpaa.2025.107982","DOIUrl":"10.1016/j.jpaa.2025.107982","url":null,"abstract":"<div><div>The main object of this article is to show the generalization of Lüroth's theorem to the case of a skew fraction field <span><math><mi>H</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span>, where <em>H</em> denotes a field of finite dimension over its center and <span><math><mi>σ</mi><mo>∈</mo><mtext>Aut</mtext><mo>(</mo><mi>H</mi><mo>)</mo></math></span> an automorphism of finite order.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107982"},"PeriodicalIF":0.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904150","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
On groups with at most five irrational conjugacy classes 关于最多有五个不合理共轭类的群体
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-28 DOI: 10.1016/j.jpaa.2025.107980
Gabriel A.L. Souza
{"title":"On groups with at most five irrational conjugacy classes","authors":"Gabriel A.L. Souza","doi":"10.1016/j.jpaa.2025.107980","DOIUrl":"10.1016/j.jpaa.2025.107980","url":null,"abstract":"<div><div>Much work has been done to study groups with few rational conjugacy classes or few rational irreducible characters. In this paper we look at the opposite extreme. Let <em>G</em> be a finite group. Given a conjugacy class <em>K</em> of <em>G</em>, we say it is <em>irrational</em> if there is some <span><math><mi>χ</mi><mo>∈</mo><mi>Irr</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> such that <span><math><mi>χ</mi><mo>(</mo><mi>K</mi><mo>)</mo><mo>∉</mo><mi>Q</mi></math></span>. One of our main results shows that, when <em>G</em> contains at most 5 irrational conjugacy classes, then <span><math><mo>|</mo><msub><mrow><mi>Irr</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>=</mo><mo>|</mo><msub><mrow><mi>Cl</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo></math></span>. This suggests some duality with the known results and open questions on groups with few rational irreducible characters. Our results are independent of the Classification of Finite Simple Groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107980"},"PeriodicalIF":0.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904148","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
Biased elementary doctrines and quotient completions 偏颇的基本原理与商完备
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-28 DOI: 10.1016/j.jpaa.2025.107983
Cipriano Junior Cioffo
{"title":"Biased elementary doctrines and quotient completions","authors":"Cipriano Junior Cioffo","doi":"10.1016/j.jpaa.2025.107983","DOIUrl":"10.1016/j.jpaa.2025.107983","url":null,"abstract":"<div><div>In this work, we fill the gap between the elementary quotient completion introduced by Maietti and Rosolini and the exact completion of a category with weak finite limits, as described by Carboni and Vitale. To achieve this, we generalize Lawvere's elementary doctrines to apply to categories with weak finite products, referring to these structures as biased elementary doctrines. We present two main constructions: the first, called strictification, produces an elementary doctrine from a biased one, while the second is an extension of the elementary quotient completion that generalizes the exact completion of a category with weak finite limits, even when weak finite products are involved.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107983"},"PeriodicalIF":0.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143905950","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
On indecomposable IYB-groups and their primes 关于不可分解的iyb群及其素数
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-28 DOI: 10.1016/j.jpaa.2025.107986
Sergio Camp-Mora , Raúl Sastriques
{"title":"On indecomposable IYB-groups and their primes","authors":"Sergio Camp-Mora ,&nbsp;Raúl Sastriques","doi":"10.1016/j.jpaa.2025.107986","DOIUrl":"10.1016/j.jpaa.2025.107986","url":null,"abstract":"<div><div>This paper investigates the mathematical properties of IYB-groups, particularly focusing on the set of primes that divide the cardinality of finite IYB-groups associated to indecomposable set-theoretic solutions of the Yang-Baxter equation. We establish a direct relationship between the primes that divide the cardinality of an IYB-group and those that divide the cardinality of the finite set on which the solution is defined. From this, we derive an upper bound for the primes dividing these IYB-groups for indecomposable solutions.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107986"},"PeriodicalIF":0.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913101","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
On the hyperfields associated to valued fields 在与值字段关联的超字段上
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-25 DOI: 10.1016/j.jpaa.2025.107985
Alessandro Linzi , Pierre Touchard
{"title":"On the hyperfields associated to valued fields","authors":"Alessandro Linzi ,&nbsp;Pierre Touchard","doi":"10.1016/j.jpaa.2025.107985","DOIUrl":"10.1016/j.jpaa.2025.107985","url":null,"abstract":"<div><div>One can associate an inverse system of valued hyperfields <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>∈</mo><mi>I</mi></mrow></msub></math></span> to a valued field in a natural way. We investigate when, conversely, such a system arises from a valued field. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields. Secondly, we describe a Hahn-like construction which yields a henselian valued field from a stringent valued hyperfield. In addition, we provide an axiomatisation of the theory of stringent valued hyperfields in a language consisting of two binary function symbols, ⊕ and ⋅, and two constant symbols, <strong>0</strong> and <strong>1</strong>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107985"},"PeriodicalIF":0.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906188","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
Silting interval reduction and 0-Auslander extriangulated categories 泥沙间隔减少和0-Auslander三角化分类
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-25 DOI: 10.1016/j.jpaa.2025.107978
Jixing Pan , Bin Zhu
{"title":"Silting interval reduction and 0-Auslander extriangulated categories","authors":"Jixing Pan ,&nbsp;Bin Zhu","doi":"10.1016/j.jpaa.2025.107978","DOIUrl":"10.1016/j.jpaa.2025.107978","url":null,"abstract":"<div><div>We give a reduction technique for silting intervals in extriangulated categories, which we call silting interval reduction. It provides a reduction technique for tilting subcategories when the extriangulated categories are exact categories.</div><div>In 0-Auslander extriangulated categories (a generalization of the well-known two-term category <span><math><msup><mrow><mi>K</mi></mrow><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo></mrow></msup><mo>(</mo><mrow><mi>proj</mi></mrow><mi>Λ</mi><mo>)</mo></math></span> for an Artin algebra Λ), we provide a reduction theory for silting objects as an application of silting interval reduction. It unifies two-term silting reduction and Iyama-Yoshino's 2-Calabi-Yau reduction. The mutation theory developed by Gorsky, Nakaoka and Palu recently can be deduced from it. Since there are bijections between the silting objects and the support <em>τ</em>-tilting modules over certain finite dimensional algebras, we show it is compatible with <em>τ</em>-tilting reduction. This compatibility theorem also unifies the two compatibility theorems obtained by Jasso in his work on <em>τ</em>-tilting reduction.</div><div>We give a new construction for 0-Auslander extriangulated categories using silting mutation, together with silting interval reduction, we obtain some results on silting quivers. Finally, we prove that <em>d</em>-Auslander extriangulated categories are related to a certain sequence of silting mutations.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107978"},"PeriodicalIF":0.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904149","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
On the injective self-maps of algebraic varieties 代数变种的内射自映射
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-25 DOI: 10.1016/j.jpaa.2025.107988
Indranil Biswas , Nilkantha Das
{"title":"On the injective self-maps of algebraic varieties","authors":"Indranil Biswas ,&nbsp;Nilkantha Das","doi":"10.1016/j.jpaa.2025.107988","DOIUrl":"10.1016/j.jpaa.2025.107988","url":null,"abstract":"<div><div>A conjecture of Miyanishi says that an endomorphism of an algebraic variety, defined over an algebraically closed field of characteristic zero, is an automorphism if the endomorphism is injective outside a closed subset of codimension at least 2. We prove the conjecture in the following cases:<ul><li><span>(1)</span><span><div>The variety is non-singular.</div></span></li><li><span>(2)</span><span><div>The variety is a surface.</div></span></li><li><span>(3)</span><span><div>The variety is locally a complete intersection that is regular in codimension 2.</div></span></li></ul> We also discuss a few instances where an endomorphism of a variety, satisfying the hypothesis of the conjecture of Miyanishi, induces an automorphism of the non-singular locus of the variety. Under additional hypotheses, we prove that the conjecture holds when the variety has only isolated singularities.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107988"},"PeriodicalIF":0.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143883219","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
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