Journal of Pure and Applied Algebra最新文献

{"title":"The based rings of two-sided cells in an affine Weyl group of type B˜3, III","authors":"Yannan Qiu","doi":"10.1016/j.jpaa.2025.107950","DOIUrl":"10.1016/j.jpaa.2025.107950","url":null,"abstract":"<div><div>We compute the based ring of the two-sided cell corresponding to the unipotent class in <span><math><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math></span> with Jordan blocks (2211). The result also verifies Lusztig's conjecture on the structure of the based rings of the two-sided cells of an affine Weyl group.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107950"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738975","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 associated graded algebras of Brauer graph algebras II: Infinite representation type","authors":"Jing Guo ,&nbsp;Yuming Liu ,&nbsp;Yu Ye","doi":"10.1016/j.jpaa.2025.107954","DOIUrl":"10.1016/j.jpaa.2025.107954","url":null,"abstract":"<div><div>Let <em>G</em> be a Brauer graph and <em>A</em> the associated Brauer graph algebra. Denote by <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> the graded algebra associated with the radical filtration of <em>A</em>. The question when <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is of finite representation type was answered in a previous paper. In the present paper, we characterize when <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is domestic in terms of the associated Brauer graph <em>G</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107954"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704492","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 derivations of free algebras over operads and the generalized divergence","authors":"Geoffrey Powell","doi":"10.1016/j.jpaa.2025.107947","DOIUrl":"10.1016/j.jpaa.2025.107947","url":null,"abstract":"<div><div>For <span><math><mi>O</mi></math></span> a reduced operad, a generalized divergence from the derivations of a free <span><math><mi>O</mi></math></span>-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the associative operad, to the double divergence of Alekseev, Kawazumi, Kuno and Naef. The generalized divergence is shown to be a 1-cocycle for the usual Lie algebra structure on derivations. These results place the previous constructions into a unified framework; moreover, they are natural with respect to the operad.</div><div>An important new ingredient is the use of naturality with respect to the category of finite-rank free modules and split monomorphisms over a commutative ring <em>R</em>. This allows the notion of torsion for such functors to be exploited.</div><div>Supposing that the ring <em>R</em> is a PID and that the operad <span><math><mi>O</mi></math></span> is binary, the main result relates the kernel of the generalized divergence to the sub Lie algebra of the Lie algebra of derivations that is generated by the elements of degree one with respect to the grading induced by arity.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107947"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683879","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 representation embedding for algebras of infinite type","authors":"R. Bautista ,&nbsp;E. Pérez ,&nbsp;L. Salmerón","doi":"10.1016/j.jpaa.2025.107955","DOIUrl":"10.1016/j.jpaa.2025.107955","url":null,"abstract":"<div><div>We show that for any finite-dimensional algebra Λ of infinite representation type, over a perfect field, there is a bounded principal ideal domain Γ and a representation embedding from <span><math><mi>Γ</mi><mtext>-</mtext><mrow><mi>mod</mi></mrow></math></span> into <span><math><mi>Λ</mi><mtext>-</mtext><mrow><mi>mod</mi></mrow></math></span>. As an application, we prove a variation of the second Brauer-Thrall conjecture: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107955"},"PeriodicalIF":0.7,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759662","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":"Ulrich bundles on double covers of projective spaces","authors":"N. Mohan Kumar ,&nbsp;Poornapushkala Narayanan ,&nbsp;A.J. Parameswaran","doi":"10.1016/j.jpaa.2025.107946","DOIUrl":"10.1016/j.jpaa.2025.107946","url":null,"abstract":"<div><div>In this article, we prove that any smooth projective variety <em>X</em> which is a double cover of the projective space <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> (<span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>) admits an Ulrich bundle. When <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, we show that on any such <em>X</em>, there is an Ulrich bundle of rank two.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107946"},"PeriodicalIF":0.7,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704493","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":"Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class","authors":"E. Javier Elizondo ,&nbsp;Alex Fink ,&nbsp;Cristhian Garay López","doi":"10.1016/j.jpaa.2025.107930","DOIUrl":"10.1016/j.jpaa.2025.107930","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span> be the complex Grassmannian of affine <em>d</em>-planes in <em>n</em>-space. We study the problem of characterizing the set of algebraic subvarieties of <span><math><mi>G</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span> invariant under the action of the maximal torus <em>T</em> and having given homology class <em>λ</em>. We give a complete answer for the case where <em>λ</em> is the class of a <em>T</em>-orbit, and partial results for other cases, using techniques inspired by matroid theory. This problem has applications to the computation of the Euler-Chow series for Grassmannians of projective lines.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107930"},"PeriodicalIF":0.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610149","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 negative answer to a Bahturin-Regev conjecture about regular algebras in positive characteristic","authors":"Lucio Centrone ,&nbsp;Plamen Koshlukov ,&nbsp;Kauê Pereira","doi":"10.1016/j.jpaa.2025.107933","DOIUrl":"10.1016/j.jpaa.2025.107933","url":null,"abstract":"<div><div>Let <span><math><mi>A</mi><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊕</mo><mo>⋯</mo><mo>⊕</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> be a decomposition of the algebra <em>A</em> as a direct sum of vector subspaces. If for every choice of the indices <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>≤</mo><mi>r</mi></math></span> there exist <span><math><msub><mrow><mi>a</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></msub></math></span> such that the product <span><math><msub><mrow><mi>a</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>⋯</mo><msub><mrow><mi>a</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mo>≠</mo><mn>0</mn></math></span>, and for every <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>≤</mo><mi>r</mi></math></span> there is a constant <span><math><mi>β</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mn>0</mn></math></span> with <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>=</mo><mi>β</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, the above decomposition is <em>regular</em>. Bahturin and Regev raised the following conjecture: suppose that the regular decomposition comes from a group grading on <em>A</em>, and form the <span><math><mi>r</mi><mo>×</mo><mi>r</mi></math></span> matrix whose <span><math><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></span>th entry equals <span><math><mi>β</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></span>. Then this matrix is invertible if and only if the decomposition is minimal (that is one cannot get a regular decomposition of <em>A</em> by coarsening the decomposition). Aljadeff and David proved that the conjecture is true in the case the base field is of characteristic 0. We prove that the conjecture does not hold for algebras over fields of positive characteristic, by constructing algebras with minimal regular decompositions such that the associated matrix is singular.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107933"},"PeriodicalIF":0.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610147","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 category of π-finite spaces","authors":"Mathieu Anel","doi":"10.1016/j.jpaa.2025.107925","DOIUrl":"10.1016/j.jpaa.2025.107925","url":null,"abstract":"<div><div>We show that the category of truncated spaces with finite homotopy invariants (<em>π</em>-finite spaces) has many of the features expected of an elementary ∞-topos. It should be thought of as the natural higher analogue of the elementary 1-topos of finite sets, with which it shares several initiality properties. The paper has also an appendix about univalent families in ∞-pretopoi.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107925"},"PeriodicalIF":0.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601847","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":"The spectrum of the real line","authors":"Jan-Paul Lerch","doi":"10.1016/j.jpaa.2025.107928","DOIUrl":"10.1016/j.jpaa.2025.107928","url":null,"abstract":"<div><div>Motivated by the study of persistence modules over the real line, we investigate the category of linear representations of a totally ordered set. We show that this category is locally coherent and we classify the indecomposable injective objects up to isomorphism. These classes form the spectrum, which we show to be homeomorphic to an ordered space. Moreover, as the spectral category turns out to be discrete, the spectrum parametrises all injective objects.</div><div>Finally, for the case of the real line we show that this topology refines the topology induced by the interleaving distance, which is known from persistence homology.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107928"},"PeriodicalIF":0.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610150","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":"Infinity categories with duality and hermitian multiplicative infinite loop space machines","authors":"Hadrian Heine,&nbsp;Alejo Lopez-Avila,&nbsp;Markus Spitzweck","doi":"10.1016/j.jpaa.2025.107929","DOIUrl":"10.1016/j.jpaa.2025.107929","url":null,"abstract":"<div><div>We show that any preadditive ∞-category with duality gives rise to a direct sum hermitian <em>K</em>-theory spectrum. This assignment is lax symmetric monoidal, thereby producing <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-ring spectra from preadditive symmetric monoidal ∞-categories with duality. To have examples of preadditive symmetric monoidal ∞-categories with duality we show that any preadditive symmetric monoidal ∞-category, in which every object admits a dual, carries a canonical duality. Moreover we classify and twist the dualities in various ways and apply our definitions for example to finitely generated projective modules over <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-ring spectra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107929"},"PeriodicalIF":0.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610145","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}