Journal of Algebra最新文献

{"title":"Classification of simple Harish-Chandra modules of the Cartan type Lie algebra S¯2","authors":"Jinxin Hu,&nbsp;Rencai Lü","doi":"10.1016/j.jalgebra.2025.07.038","DOIUrl":"10.1016/j.jalgebra.2025.07.038","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mover><mrow><mi>S</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub></math></span> be the Lie algebra of vector fields on <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with constant divergence. In this paper, we classify all simple Harish-Chandra modules of <span><math><msub><mrow><mover><mrow><mi>S</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub></math></span> including bounded and non-bounded simple Harish-Chandra modules. In simple terms, any simple Harish-Chandra module of <span><math><msub><mrow><mover><mrow><mi>S</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub></math></span> is isomorphic to a tensor module <span><math><mi>F</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></span> or its simple sub-quotient where <em>P</em> is a simple weight <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>:</mo><mo>=</mo><mi>C</mi><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mfrac><mrow><mo>∂</mo></mrow><mrow><mo>∂</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo></mrow><mrow><mo>∂</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>]</mo><mo>)</mo></math></span> module and <em>M</em> is a simple weight <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> module.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 828-851"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830076","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}

{"title":"On the second minimum average character degree of finite nonsolvable groups","authors":"Kamal Aziziheris ,&nbsp;Mahnaz Eivazzadeh","doi":"10.1016/j.jalgebra.2025.07.029","DOIUrl":"10.1016/j.jalgebra.2025.07.029","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>acd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the average character degree of a finite group <em>G</em>. It has been proved that <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><mrow><mi>acd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mi>G</mi><mo>∈</mo><mi>A</mi><mo>}</mo><mo>=</mo><mrow><mi>acd</mi></mrow><mo>(</mo><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub><mo>)</mo><mo>=</mo><mfrac><mrow><mn>16</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span>, where <span><math><mi>A</mi></math></span> is the family of all finite nonsolvable groups. In this paper, we assume that <span><math><mi>B</mi></math></span> is the family of all finite nonsolvable groups <em>G</em> having a nonabelian minimal normal subgroup not isomorphic to <span><math><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub></math></span>. We prove that <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><mrow><mi>acd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mi>G</mi><mo>∈</mo><mi>B</mi><mo>}</mo><mo>=</mo><mrow><mi>acd</mi></mrow><mo>(</mo><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>)</mo><mo>=</mo><mfrac><mrow><mn>14</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>. While we show that the second minimum average character degree of arbitrary nonsolvable groups does not exist, we classify all finite groups with <span><math><mrow><mi>acd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>&lt;</mo><mn>14</mn><mo>/</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 26-45"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831466","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}

{"title":"Real simple modules over simply-laced quantum affine algebras and categorifications of cluster algebras","authors":"Bing Duan ,&nbsp;Ralf Schiffler","doi":"10.1016/j.jalgebra.2025.07.043","DOIUrl":"10.1016/j.jalgebra.2025.07.043","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi></math></span> be the category of finite-dimensional modules over a simply-laced quantum affine algebra <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mover><mrow><mi>g</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span>. For any height function <em>ξ</em> and <span><math><mi>ℓ</mi><mo>∈</mo><msub><mrow><mi>Z</mi></mrow><mrow><mo>≥</mo><mn>1</mn></mrow></msub></math></span>, we introduce certain subcategories <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> of <span><math><mi>C</mi></math></span>, and prove that the quantum Grothendieck ring <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>(</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup><mo>)</mo></math></span> of <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> admits a quantum cluster algebra structure. We classify the real prime simple modules (call them the Hernandez–Leclerc modules) in <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> in terms of their highest <em>l</em>-weight monomials by relating this subcategory <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> to the cluster category <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> of the Dynkin quiver given by <em>ξ</em>. For any <em>ℓ</em>, we formulate the modified Hernandez-Leclerc conjectures, and prove them for the subcategories <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>ℓ</mi></mrow><mrow><mo>≤</mo><mi>ξ</mi></mrow></msubsup></math></span> whose Grothendieck rings are cluster algebras of finite type.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 608-672"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865360","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}

{"title":"Bounding regularity of FIm-modules","authors":"Wee Liang Gan ,&nbsp;Khoa Ta","doi":"10.1016/j.jalgebra.2025.07.037","DOIUrl":"10.1016/j.jalgebra.2025.07.037","url":null,"abstract":"<div><div>Let FI be a skeleton of the category of finite sets and injective maps, and <span><math><msup><mrow><mi>FI</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> the product of <em>m</em> copies of FI. We prove that if an <span><math><msup><mrow><mi>FI</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>-module is generated in degree ⩽<em>d</em> and related in degree ⩽<em>r</em>, then its regularity is bounded above by a function of <em>m</em>, <em>d</em>, and <em>r</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 86-111"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831469","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}

{"title":"Tied–boxed algebras","authors":"Diego Arcis ,&nbsp;Jorge Espinoza","doi":"10.1016/j.jalgebra.2025.07.039","DOIUrl":"10.1016/j.jalgebra.2025.07.039","url":null,"abstract":"<div><div>We introduce two new algebras that we call <em>tied–boxed Hecke algebra</em> and <em>tied–boxed Temperley–Lieb algebra</em>. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second one is a tied-version of the well known Temperley–Lieb algebra. We study their representation theory and give cellular bases for them. Furthermore, we explore a strong connection between the tied–boxed Temperley–Lieb algebra and the so-called partition Temperley–Lieb algebra given by Juyumaya. Also, we show that both structures inherit diagrammatic interpretations from a new class of monoids that we call <em>boxed ramified monoids</em>. Additionally, we give presentations for the singular part of the ramified symmetric monoid and for the boxed ramified monoid associated to the Brauer monoid.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 112-159"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831470","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}

{"title":"Tensor extriangulated categories","authors":"Raphael Bennett-Tennenhaus ,&nbsp;Isambard Goodbody ,&nbsp;Janina C. Letz ,&nbsp;Amit Shah","doi":"10.1016/j.jalgebra.2025.07.041","DOIUrl":"10.1016/j.jalgebra.2025.07.041","url":null,"abstract":"<div><div>A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor <span><math><mi>A</mi><mo>×</mo><mi>B</mi><mo>→</mo><mi>C</mi></math></span>, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 361-405"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831475","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}

{"title":"Equational theories of the Boolean matrix monoid BRn with involutions","authors":"Wen-Ting Zhang,&nbsp;Meng Gao,&nbsp;Yan-Feng Luo","doi":"10.1016/j.jalgebra.2025.07.045","DOIUrl":"10.1016/j.jalgebra.2025.07.045","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the monoid of all &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; Boolean matrices with 1s on the main diagonal. It is known that &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; can be identified with the monoid of all reflexive binary relations on an &lt;em&gt;n&lt;/em&gt;-element set under composition. The monoid &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; admits two natural unary operations: the transposition &lt;sup&gt;&lt;em&gt;T&lt;/em&gt;&lt;/sup&gt; and the skew transposition &lt;sup&gt;&lt;em&gt;D&lt;/em&gt;&lt;/sup&gt;, which makes &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; an involutory monoid. Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (resp. &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) be the submonoid of &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; consisting of all &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; upper triangular Boolean matrices with 1s on the main diagonal (resp. all convex Boolean matrices) and &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; the monoid of all convex upper triangular Boolean matrices. Denote by &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; the double Catalan monoid which is a submonoid of &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;In this paper, we explore equational theories of the involutory monoids &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Firstly, we have completely solved the finite basis problems for &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. It is shown that the involutory monoid &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is finitely based if and only if &lt;sp","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 225-270"},"PeriodicalIF":0.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831472","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}

{"title":"Characters of Ariki–Koike algebras","authors":"Deke Zhao","doi":"10.1016/j.jalgebra.2025.07.023","DOIUrl":"10.1016/j.jalgebra.2025.07.023","url":null,"abstract":"<div><div>In this paper, we prove the Regev formula for the characters of the Ariki–Koike algebras by applying the Schur–Sergeev reciprocity between quantum superalgebras and Ariki–Koike algebras. As a corollary, we derive the Regev formula for the characters of the complex reflection group of type <span><math><mi>G</mi><mo>(</mo><mi>m</mi><mo>,</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></math></span>, generalizing the Regev formula for the symmetric groups due to A. Regev (2013) <span><span>[19]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 773-791"},"PeriodicalIF":0.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813982","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}

{"title":"Brauer's 14th Problem and Dyson's tenfold way","authors":"Dmitriy Rumynin ,&nbsp;James Taylor","doi":"10.1016/j.jalgebra.2025.07.026","DOIUrl":"10.1016/j.jalgebra.2025.07.026","url":null,"abstract":"<div><div>We consider Brauer's 14th Problem in the context of <em>Real</em> structures on finite groups and their antilinear representations. The problem is to count the number of characters of each different type using “group theory”. While Brauer's original problem deals only with three types (real, complex and quaternionic), here we consider the ten types coming from Dyson's tenfold way.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 463-473"},"PeriodicalIF":0.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861234","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}

{"title":"On the fibers of the principal minor map and an application to stable polynomials","authors":"Abeer Al Ahmadieh","doi":"10.1016/j.jalgebra.2025.07.030","DOIUrl":"10.1016/j.jalgebra.2025.07.030","url":null,"abstract":"<div><div>This paper explores the fibers of the principal minor map over an arbitrary field. The principal minor map assigns to each <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrix the <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>-vector of its principal minors. In 1984, Hartfiel and Loewy proposed a condition that was sufficient to ensure that the fiber of the principal minor map is a single point up to diagonal equivalence. Loewy later improved upon this condition in 1986. In this paper, we provide a necessary and sufficient condition for the fiber to be a point up to diagonal equivalence. Additionally, we establish a connection between the reducibility of a matrix and the reducibility of its determinantal representation. Using this connection, we fully characterize the fibers that contain a symmetric or Hermitian matrix in the space of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices over any field. We also use these techniques to answer a question of Borcea, Brändén, and Liggett concerning real stable matrices.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 46-61"},"PeriodicalIF":0.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831467","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}