Journal of Algebra最新文献

{"title":"Quadratic points on X0(163)","authors":"Philippe Michaud-Jacobs ,&nbsp;Filip Najman","doi":"10.1016/j.jalgebra.2024.11.027","DOIUrl":"10.1016/j.jalgebra.2024.11.027","url":null,"abstract":"<div><div>We determine all the quadratic points on the genus 13 modular curve <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>163</mn><mo>)</mo></math></span>, thus completing the answer to a recent question of Banwait, the second-named author, and Padurariu. In doing so, we investigate a curious phenomenon involving a cubic point with complex multiplication on the curve <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>163</mn><mo>)</mo></math></span>. This cubic point prevents us, due to computational restraints, from directly applying the state-of-the-art Atkin–Lehner sieve for computing quadratic points on modular curves <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span>. To overcome this issue, we introduce a technique which allows us to work with the Jacobian of curves modulo primes by directly computing linear equivalence relations between divisors.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 279-288"},"PeriodicalIF":0.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152729","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":"Computing isogenies from modular equations in genus two","authors":"Jean Kieffer ,&nbsp;Aurel Page ,&nbsp;Damien Robert","doi":"10.1016/j.jalgebra.2024.11.029","DOIUrl":"10.1016/j.jalgebra.2024.11.029","url":null,"abstract":"<div><div>Consider two genus 2 curves over a field whose Jacobians are linked by an isogeny of known type: either an <em>ℓ</em>-isogeny or, in the real multiplication case, an isogeny with cyclic kernel. We present a completely algebraic algorithm to compute this isogeny using modular equations of either Siegel or Hilbert type. An essential step of independent interest is to construct an explicit Kodaira–Spencer isomorphism for principally polarized abelian surfaces.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 331-386"},"PeriodicalIF":0.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152730","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":"Group gradings on triangularizable algebras","authors":"Waldeck Schützer ,&nbsp;Felipe Yukihide Yasumura","doi":"10.1016/j.jalgebra.2024.11.026","DOIUrl":"10.1016/j.jalgebra.2024.11.026","url":null,"abstract":"<div><div>Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a kind of algebra that is neither simple nor finite-dimensional, aiming to classify the group gradings on triangularizable algebras as defined by Mesyan in 2019. The topology of infinite-dimensional algebras, along with the role of idempotent elements, plays a crucial role in our findings, leading to new insights and a deeper understanding of their structure.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 446-474"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152655","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":"Double extension of flat pseudo-Riemannian F-Lie algebras","authors":"Alexander Torres-Gomez ,&nbsp;Fabricio Valencia","doi":"10.1016/j.jalgebra.2024.11.021","DOIUrl":"10.1016/j.jalgebra.2024.11.021","url":null,"abstract":"<div><div>We define the concept of a flat pseudo-Riemannian <em>F</em>-Lie algebra and construct its corresponding double extension. This algebraic structure can be interpreted as the infinitesimal analogue of a Frobenius Lie group devoid of Euler vector fields. We show that the double extension provides a framework for generating all weakly flat Lorentzian non-abelian bi-nilpotent <em>F</em>-Lie algebras possessing one-dimensional light-cone subspaces. A similar result can be established for nilpotent Lie algebras equipped with flat scalar products of signature <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo></math></span> where <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. Furthermore, we use this technique to construct Poisson algebras exhibiting compatibility with flat scalar products.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 1-27"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152652","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":"Representations of N∞-type combinatorial categories","authors":"Zhenxing Di ,&nbsp;Liping Li ,&nbsp;Li Liang","doi":"10.1016/j.jalgebra.2024.11.020","DOIUrl":"10.1016/j.jalgebra.2024.11.020","url":null,"abstract":"<div><div>In this paper we consider representations of certain combinatorial categories, including the poset <span><math><mi>D</mi></math></span> of positive integers and division, the Young lattice <span><math><mi>Y</mi></math></span> of partitions of finite sets, the opposite category of the orbit category <span><math><mi>Z</mi></math></span> of <span><math><mo>(</mo><mi>Z</mi><mo>,</mo><mo>+</mo><mo>)</mo></math></span> with respect to nontrivial subgroups, and the category <span><math><mi>CI</mi></math></span> of finite cyclic groups and injective homomorphisms. We describe explicit upper bounds for homological degrees of their representations, and deduce that finitely presented representations (resp., representations presented in finite degrees) over a field form abelian subcategories of the representation categories. We also give an explicit description for the category of sheaves over the ringed atomic site <span><math><mo>(</mo><mi>Z</mi><mo>,</mo><mspace></mspace><msub><mrow><mi>J</mi></mrow><mrow><mi>a</mi><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><munder><mrow><mi>C</mi></mrow><mo>_</mo></munder><mo>)</mo></math></span>, and show that irreducible sheaves are parameterized by primitive roots of the unit.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 47-81"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152654","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":"Finitely generated normal pro-C subgroups in right angled Artin pro-C groups","authors":"Dessislava H. Kochloukova ,&nbsp;Pavel A. Zalesskii","doi":"10.1016/j.jalgebra.2024.11.025","DOIUrl":"10.1016/j.jalgebra.2024.11.025","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi></math></span> be a class of finite groups closed for subgroups, quotient groups and extensions. Let Γ be a finite simplicial graph and <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>Γ</mi></mrow></msub></math></span> be the corresponding pro-<span><math><mi>C</mi></math></span> RAAG. We show that if <em>N</em> is a non-trivial finitely generated, normal, full pro-<span><math><mi>C</mi></math></span> subgroup of <em>G</em> then <span><math><mi>G</mi><mo>/</mo><mi>N</mi></math></span> is finite-by-abelian. In the pro-<em>p</em> case we show a criterion for <em>N</em> to be of type <span><math><mi>F</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> when <span><math><mi>G</mi><mo>/</mo><mi>N</mi><mo>≃</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. Furthermore for <span><math><mi>G</mi><mo>/</mo><mi>N</mi></math></span> infinite abelian we show that <em>N</em> is finitely generated if and only if every normal closed subgroup <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>◃</mo><mi>G</mi></math></span> containing <em>N</em> with <span><math><mi>G</mi><mo>/</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≃</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is finitely generated. For <span><math><mi>G</mi><mo>/</mo><mi>N</mi></math></span> infinite abelian with <em>N</em> weakly discretely embedded in <em>G</em> we show that <em>N</em> is of type <span><math><mi>F</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> if and only if every <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>⩽</mo><mi>G</mi></math></span> containing <em>N</em> with <span><math><mi>G</mi><mo>/</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≃</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is of type <span><math><mi>F</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 475-506"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152656","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":"Content and Q-sequences in mixed characteristic local rings","authors":"Olivia Strahan","doi":"10.1016/j.jalgebra.2024.11.022","DOIUrl":"10.1016/j.jalgebra.2024.11.022","url":null,"abstract":"<div><div>It is proved that a system of parameters is always a Q-sequence (in the sense of Hochster and Huneke) for several classes of mixed characteristic rings: rings in which the characteristic of the residue field is a nilpotent element, and mixed characteristic analogues of Stanley-Reisner rings, semigroup rings, and toric face rings.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 633-656"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152657","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 polynomials depending on coefficients of Puiseux parametrizations","authors":"Beata Gryszka,&nbsp;Janusz Gwoździewicz","doi":"10.1016/j.jalgebra.2024.11.024","DOIUrl":"10.1016/j.jalgebra.2024.11.024","url":null,"abstract":"<div><div>Every irreducible germ of singular complex plane analytic curve at the origin can be described in two ways in a given coordinate system: by a parametrization <span><math><mi>x</mi><mo>=</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>y</mi><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup></math></span> or by an equation <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> where <span><math><mi>f</mi><mo>=</mo><mo>∑</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><msup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msup><msup><mrow><mi>Y</mi></mrow><mrow><mi>j</mi></mrow></msup></math></span> is a complex power series in two variables. We show that every polynomial condition on the coefficients of a parametrization is, under some natural invariance assumptions, equivalent with a polynomial condition on the coefficients of <em>f</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 289-307"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152711","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":"Equivariant algebraic and semi-algebraic geometry of infinite affine space","authors":"Mario Kummer ,&nbsp;Cordian Riener","doi":"10.1016/j.jalgebra.2024.11.016","DOIUrl":"10.1016/j.jalgebra.2024.11.016","url":null,"abstract":"<div><div>We study <span><math><mi>Sym</mi><mo>(</mo><mo>∞</mo><mo>)</mo></math></span>-orbit closures of non-necessarily closed points in the Zariski spectrum of the infinite polynomial ring <span><math><mi>C</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>:</mo><mspace></mspace><mi>i</mi><mo>∈</mo><mi>N</mi><mo>,</mo><mspace></mspace><mi>j</mi><mo>∈</mo><mo>[</mo><mi>n</mi><mo>]</mo><mo>]</mo></math></span>. Among others, we characterize invariant prime ideals in this ring. Furthermore, we study projections of basic equivariant semi-algebraic sets defined by <span><math><mi>Sym</mi><mo>(</mo><mo>∞</mo><mo>)</mo></math></span> orbits of polynomials in <span><math><mi>R</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>:</mo><mspace></mspace><mi>i</mi><mo>∈</mo><mi>N</mi><mo>,</mo><mspace></mspace><mi>j</mi><mo>∈</mo><mo>[</mo><mi>n</mi><mo>]</mo><mo>]</mo></math></span>. For <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span> we prove a quantifier elimination type result which fails for <span><math><mi>n</mi><mo>&gt;</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 28-46"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143152653","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}

{"title":"A Burnside ring for monoids","authors":"Jeremy Weissmann","doi":"10.1016/j.jalgebra.2024.10.052","DOIUrl":"10.1016/j.jalgebra.2024.10.052","url":null,"abstract":"<div><div>We define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we describe the monoid-theoretic correlates of orbits and their automorphisms, then prove a structure theorem for a broad class of monoids that allows us to write the Burnside ring as a direct product of Burnside rings of groups. Finally, we define a monoid-theoretic correlate of the table of marks, and show that the Burnside algebra over <span><math><mi>Q</mi></math></span> is semisimple.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"666 ","pages":"Pages 213-250"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128140","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}