Journal of Algebra最新文献

{"title":"A generalisation of the pencil of Kuribayashi-Komiya quartics","authors":"Valentina Moreno Vega,&nbsp;Sebastián Reyes-Carocca","doi":"10.1016/j.jalgebra.2026.01.033","DOIUrl":"10.1016/j.jalgebra.2026.01.033","url":null,"abstract":"<div><div>The pencil of Kuribayashi-Komiya quartics<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>+</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>+</mo><mi>t</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mtext> where </mtext><mi>t</mi><mo>∈</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span></span></span> is a complex one-dimensional family of Riemann surfaces of genus three endowed with a group of automorphisms isomorphic to the symmetric group of order twenty-four. This pencil has been extensively studied from different points of view.</div><div>This paper is aimed at studying, for each prime number <span><math><mi>p</mi><mo>⩾</mo><mn>5</mn></math></span>, the pencil of <em>generalised Kuribayashi-Komiya curves</em> <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, given by the curves<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>+</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>+</mo><mi>t</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>p</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>p</mi></mrow></msup><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>p</mi></mrow></msup><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mtext> where </mtext><mi>t</mi><mo>∈</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>.</mo></math></span></span></span></div><div>We determine the full automorphism group <em>G</em> of each smooth member <span><math><mi>X</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and study the action of <em>G</em> and of its subgroups on <em>X</em>. In particular, we show that no member of the pencil is hyperelliptic. As a by-product, we derive a classification of all those Riemann surfaces of genus <span><math><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span> that are endowed with a group of automorphisms isomorphic to the full automorphism group of the generic smooth member of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 359-380"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171955","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":"A polynomial basis for the stuffle algebra and its applications","authors":"Tuan Ngo Dac ,&nbsp;Gia Vuong Nguyen Chu ,&nbsp;Lan Huong Pham","doi":"10.1016/j.jalgebra.2026.01.026","DOIUrl":"10.1016/j.jalgebra.2026.01.026","url":null,"abstract":"<div><div>In this paper we construct a polynomial basis for the stuffle algebra over a field of characteristic <span><math><mi>p</mi><mo>&gt;</mo><mn>0</mn></math></span>. As an application we derive the transcendence degree for multiple zeta values in positive characteristic of small weights. To our knowledge, the only known result is the case of weight 2 which was proved by Mishiba using a completely different approach.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 221-244"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172047","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":"Lannes' T-functor and mod-p cohomology of profinite groups","authors":"Marco Boggi","doi":"10.1016/j.jalgebra.2026.01.024","DOIUrl":"10.1016/j.jalgebra.2026.01.024","url":null,"abstract":"<div><div>The Lannes-Quillen theorem relates the mod-<em>p</em> cohomology of a finite group <em>G</em> with the mod-<em>p</em> cohomology of centralizers of abelian elementary <em>p</em>-subgroups of <em>G</em>, for <span><math><mi>p</mi><mo>&gt;</mo><mn>0</mn></math></span> a prime number. This theorem was extended to profinite groups whose mod-<em>p</em> cohomology algebra is finitely generated by Henn. In a weaker form, the Lannes-Quillen theorem was then extended by Symonds to arbitrary profinite groups. Building on Symonds' result, we formulate and prove a full version of this theorem for all profinite groups. For this purpose, we develop a theory of products for families of discrete torsion modules, parameterized by a profinite space<span><span>¹</span></span>, which is dual, in a very precise sense, to the theory of coproducts for families of profinite modules, parameterized by a profinite space, developed by Haran, Melnikov and Ribes. In the last section, we give applications to the problem of conjugacy separability of <em>p</em>-torsion elements and finite <em>p</em>-subgroups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 109-147"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172045","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":"Three homological invariants under cleft extensions","authors":"Yajun Ma ,&nbsp;Junling Zheng ,&nbsp;Yu-Zhe Liu","doi":"10.1016/j.jalgebra.2026.01.032","DOIUrl":"10.1016/j.jalgebra.2026.01.032","url":null,"abstract":"<div><div>In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 287-323"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172099","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":"Character tables are ideal Perron similarities","authors":"David Z. Gershnik,&nbsp;Alexander J. Lewis,&nbsp;Pietro Paparella","doi":"10.1016/j.jalgebra.2026.02.004","DOIUrl":"10.1016/j.jalgebra.2026.02.004","url":null,"abstract":"<div><div>An invertible matrix is called a <em>Perron similarity</em> if it diagonalizes an irreducible, nonnegative matrix. Each Perron similarity gives a nontrivial polyhedral cone, called the <em>spectracone</em>, and polytope, called the <em>spectratope</em>, of realizable spectra (thought of as vectors in complex Euclidean space). A Perron similarity is called <em>ideal</em> if its spectratope coincides with the conical hulls of its rows. Identifying ideal Perron similarities is of great interest in the pursuit of the longstanding <em>nonnegative inverse eigenvalue problem</em>.</div><div>In this work, it is shown that the character table of a finite group is an ideal Perron similarity. In addition to expanding ideal Perron similarities to include a broad class of matrices, the results unify previous works into a single, theoretical framework.</div><div>It is demonstrated that the spectracone can be described by finitely-many group-theoretic inequalities. When the character table is real, we derive a group-theoretic formula for the volume of the projected Perron spectratope, which is a simplex. Finally, an implication for further research is given.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 782-800"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385429","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":"Baker-Beynon duality beyond semisimplicity","authors":"Luca Carai ,&nbsp;Serafina Lapenta ,&nbsp;Luca Spada","doi":"10.1016/j.jalgebra.2026.02.002","DOIUrl":"10.1016/j.jalgebra.2026.02.002","url":null,"abstract":"<div><div>Combining tools from category theory, model theory, and non-standard analysis we extend Baker-Beynon dualities to the classes of <em>all</em> Abelian <em>ℓ</em>-groups and <em>all</em> Riesz spaces (also known as vector lattices). The extended dualities have a strong geometrical flavor, as they involve a non-standard version of the category of polyhedral cones and piecewise (homogeneous) linear maps between them. We further show that our dualities are induced by the functor <span>Spec</span>, once it is understood how to endow it with “coordinates” in some ultrapower <span><math><mi>U</mi></math></span> of <span><math><mi>R</mi></math></span>. This also allows us to characterize the topological spaces arising as spectra of Abelian <em>ℓ</em>-groups and Riesz spaces as certain subspaces of <span><math><msup><mrow><mi>U</mi></mrow><mrow><mi>κ</mi></mrow></msup></math></span> endowed with the Zariski topology given by definable functions in their respective languages. Furthermore, we provide some applications of the extended duality by characterizing, in geometrical terms, semisimplicity, Archimedeanity, and the existence of weak and strong order-units. Finally, we show that our dualities afford a neat and simpler proof of Panti's celebrated characterization of the prime ideals in free Abelian <em>ℓ</em>-groups and Riesz spaces.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 730-781"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385430","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":"The ring of differential operators on a quantized flag manifold","authors":"Toshiyuki Tanisaki","doi":"10.1016/j.jalgebra.2026.01.023","DOIUrl":"10.1016/j.jalgebra.2026.01.023","url":null,"abstract":"<div><div>We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra (<em>q</em>-analogue of boson).</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 1-28"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098441","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":"The splitting of generalisations of the Fadell-Neuwirth short exact sequence","authors":"Daciberg Lima Gonçalves ,&nbsp;John Guaschi ,&nbsp;Carolina de Miranda e Pereiro","doi":"10.1016/j.jalgebra.2026.01.039","DOIUrl":"10.1016/j.jalgebra.2026.01.039","url":null,"abstract":"<div><div>We study some generalisations to mixed braid groups of the Fadell-Neuwirth short exact sequence and the possible splitting of this sequence. In certain cases, we determine conditions under which the projection from the mixed braid group <span><math><msub><mrow><mi>B</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> to <span><math><msub><mrow><mi>B</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mo>−</mo><mi>q</mi></mrow></msub></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> admits a section, where <em>M</em> is either the torus or the Klein bottle, <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><mi>q</mi><mo>∈</mo><mi>N</mi></math></span>, and <span><math><mn>1</mn><mo>≤</mo><mi>q</mi><mo>≤</mo><mi>k</mi><mo>−</mo><mn>1</mn></math></span>. For <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> and <span><math><mi>q</mi><mo>=</mo><mi>k</mi><mo>−</mo><mn>1</mn></math></span>, we show that this projection admits a section if and only if <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> divides <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for all <span><math><mi>i</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi></math></span>. We present some partial conclusions in the case <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>q</mi><mo>=</mo><mn>1</mn></math></span>. To obtain our results, we compute and make use of suitable mixed braid groups of <em>M</em>, as well as certain key quotients that play a central rôle in our analysis.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 629-675"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172051","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 complete integral closedness of the p-adic completion of absolute integral closure","authors":"Raymond Heitmann ,&nbsp;Linquan Ma","doi":"10.1016/j.jalgebra.2026.01.037","DOIUrl":"10.1016/j.jalgebra.2026.01.037","url":null,"abstract":"<div><div>Fix a prime <em>p</em> and let <span><math><mo>(</mo><mi>R</mi><mo>,</mo><mi>m</mi><mo>)</mo></math></span> be a Noetherian complete local domain of mixed characteristic <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span> with fraction field <em>K</em>. Let <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> denote the absolute integral closure of <em>R</em>, which is the integral closure of <em>R</em> in an algebraic closure <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span> of <em>K</em>. The first author has shown that <span><math><mover><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>, the <em>p</em>-adic completion of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, is an integral domain. In this paper, we prove that <span><math><mover><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is completely integrally closed in <span><math><mover><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mo>ˆ</mo></mrow></mover><msub><mrow><mo>⊗</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></msub><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span>, but <span><math><mover><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is not completely integrally closed in its own fraction field when <span><math><mi>dim</mi><mo>⁡</mo><mo>(</mo><mi>R</mi><mo>)</mo><mo>≥</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 245-262"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172048","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":"Deformations and homotopy theory of Nijenhuis associative algebras","authors":"Chao Song ,&nbsp;Kai Wang ,&nbsp;Yuanyuan Zhang ,&nbsp;Guodong Zhou","doi":"10.1016/j.jalgebra.2025.12.032","DOIUrl":"10.1016/j.jalgebra.2025.12.032","url":null,"abstract":"<div><div>This paper is the first in a series of works devoted to an operadic study of Nijenhuis structures, focusing on Nijenhuis associative algebras. We introduce the concept of homotopy Nijenhuis associative algebras and demonstrate that the differential graded (=dg) operad <span><math><msub><mrow><mi>NjA</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> governing these structures serves as the minimal model of the operad <span><math><mi>NjA</mi></math></span> for Nijenhuis associative algebras. Additionally, we determine the Koszul dual homotopy cooperad of <span><math><mi>NjA</mi></math></span>. We construct an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra that controls the simultaneous deformations of associative products and Nijenhuis operators. The Maurer-Cartan elements of this <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra correspond bijectively to Nijenhuis associative algebra structures. From this, we derive a cochain complex (deformation complex) and an associated cohomology theory of Nijenhuis associative algebras. Finally, we explore the connection between homotopy relative Rota-Baxter associative algebras of weight 0 and homotopy Nijenhuis associative algebras. A sequel to this work will extend the study to Nijenhuis Lie algebras, with applications to Nijenhuis geometry.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 148-184"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172046","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}