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Journal of Pure and Applied Algebra最新文献

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Spectral excision and descent for almost perfect complexes 几乎完美复合体的光谱切除和下降
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-18 DOI: 10.1016/j.jpaa.2025.108033
Chang-Yeon Chough
{"title":"Spectral excision and descent for almost perfect complexes","authors":"Chang-Yeon Chough","doi":"10.1016/j.jpaa.2025.108033","DOIUrl":"10.1016/j.jpaa.2025.108033","url":null,"abstract":"<div><div>We show that almost perfect complexes of commutative ring spectra satisfy excision and <em>h</em>-descent. These results generalize Milnor excision for perfect complexes of ordinary commutative rings and <em>h</em>-descent for almost perfect complexes of locally noetherian derived stacks by Halpern-Leistner and Preygel, respectively.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108033"},"PeriodicalIF":0.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338573","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 completed tensor product of two preadic algebras over a field 域上两个预进代数的完全张量积
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-17 DOI: 10.1016/j.jpaa.2025.108032
Mohamed Tabaâ
{"title":"On the completed tensor product of two preadic algebras over a field","authors":"Mohamed Tabaâ","doi":"10.1016/j.jpaa.2025.108032","DOIUrl":"10.1016/j.jpaa.2025.108032","url":null,"abstract":"<div><div>Our aim in this paper is to study the problem of the transfer of the properties of two preadic noetherian algebras over a field to their completed tensor product.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108032"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338426","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 universal Drinfeld–Yetter algebra 关于普遍的Drinfeld-Yetter代数
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-17 DOI: 10.1016/j.jpaa.2025.108035
Andrea Rivezzi
{"title":"On the universal Drinfeld–Yetter algebra","authors":"Andrea Rivezzi","doi":"10.1016/j.jpaa.2025.108035","DOIUrl":"10.1016/j.jpaa.2025.108035","url":null,"abstract":"<div><div>The universal Drinfeld–Yetter algebra is an associative algebra whose co–Hochschild cohomology controls the existence of quantization functors of Lie bialgebras, such as the renowned one due to Etingof and Kazhdan. It was initially introduced by Enriquez, and later re-interpreted by Appel and Toledano Laredo as an algebra of endomorphisms in the colored PROP of a Drinfeld–Yetter module over a Lie bialgebra. Its vector space and algebra structure present a deep and mysterious connection with symmetric groups of all orders. In this paper, we provide an explicit formula for its structure constants in terms of certain combinatorial diagrams, which we term Drinfeld–Yetter looms.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108035"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322582","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
Degree bounds for rational generators of invariant fields of finite abelian groups 有限阿贝尔群不变域的有理发生器的度界
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-17 DOI: 10.1016/j.jpaa.2025.108029
Ben Blum-Smith
{"title":"Degree bounds for rational generators of invariant fields of finite abelian groups","authors":"Ben Blum-Smith","doi":"10.1016/j.jpaa.2025.108029","DOIUrl":"10.1016/j.jpaa.2025.108029","url":null,"abstract":"<div><div>We study degree bounds on rational but not necessarily polynomial generators for the field <span><math><mi>k</mi><msup><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow><mrow><mi>G</mi></mrow></msup></math></span> of rational invariants of a linear action of a finite abelian group. We show that lattice-theoretic methods used recently by the author and collaborators to study polynomial generators for the same field largely carry over, after minor modifications to the arguments. It then develops that the specific degree bounds found in that setting also carry over.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108029"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314439","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
Ind-completion and accessibility of functor categories 函子类别的补全和可访问性
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-17 DOI: 10.1016/j.jpaa.2025.108030
Simon Henry
{"title":"Ind-completion and accessibility of functor categories","authors":"Simon Henry","doi":"10.1016/j.jpaa.2025.108030","DOIUrl":"10.1016/j.jpaa.2025.108030","url":null,"abstract":"<div><div>We investigate under which conditions the <em>κ</em>-Ind completion of a functor category <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>I</mi></mrow></msup></math></span> is equivalent to the category of functors from <em>I</em> to the <em>κ</em>-Ind completion of <em>C</em>. A published result implies this is true for any Cauchy complete category <em>C</em> and <em>κ</em>-small category <em>I</em>, but we show that this is not the case in general. We prove two results that seem to cover all applications of this incorrect theorem we could find in the literature: The result holds if <em>C</em> has <em>κ</em>-small colimits and <em>I</em> is <em>κ</em>-small, or if <em>C</em> is an arbitrary category and <em>I</em> is well-founded and <em>κ</em>-small. In both cases, we show that the conditions are optimal in the sense that the result holds for all <em>C</em> if and only if <em>I</em> satisfies the given assumption.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108030"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338427","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
Orbit separation and stratification by isotropy classes of piezoelectricity tensors 压电张量各向同性类的轨道分离和分层
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-17 DOI: 10.1016/j.jpaa.2025.108034
Evelyne Hubert, Martin Jalard
{"title":"Orbit separation and stratification by isotropy classes of piezoelectricity tensors","authors":"Evelyne Hubert,&nbsp;Martin Jalard","doi":"10.1016/j.jpaa.2025.108034","DOIUrl":"10.1016/j.jpaa.2025.108034","url":null,"abstract":"<div><div>We explore an innovative method to compute separating invariants in a real G-variety <span><math><mi>V</mi></math></span>. A refinement of Seshadri slice Lemma enables us to decompose <span><math><mi>V</mi></math></span> into a union of stable subsets <span><math><mi>G</mi><mo>⋅</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊔</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>⊔</mo><mi>G</mi><mo>⋅</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>. This reduces the problem to separating the orbits in the slices <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for their normalizers <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&lt;</mo><mi>G</mi></math></span>. This sequencing allows also to identify efficiently the isotropy class of any point. After the presentation of three types of Seshadri slices for representations of <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>, we apply the method to the space of piezoelectricity tensors <span><math><mi>P</mi><mrow><mi>iez</mi></mrow></math></span>. This provides a separating set of low cardinality and a complete stratification of <span><math><mi>P</mi><mrow><mi>iez</mi></mrow></math></span> by isotropy classes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108034"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321961","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
Classification of aut-fixed subgroups in free-abelian times surface groups 自由阿贝尔曲面群中非固定子群的分类
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-10 DOI: 10.1016/j.jpaa.2025.108028
Jialin Lei, Peng Wang, Qiang Zhang
{"title":"Classification of aut-fixed subgroups in free-abelian times surface groups","authors":"Jialin Lei,&nbsp;Peng Wang,&nbsp;Qiang Zhang","doi":"10.1016/j.jpaa.2025.108028","DOIUrl":"10.1016/j.jpaa.2025.108028","url":null,"abstract":"<div><div>In this paper, we are concerned with the direct product <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>Σ</mi><mo>)</mo><mo>×</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> for Σ a compact orientable surface with negative Euler characteristic, and give a complete classification of its fixed subgroups of automorphisms. As a corollary, we show that <em>G</em> contains, up to isomorphism, infinitely many fixed subgroups of automorphisms if and only if <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>, which is a contrast to that of hyperbolic groups. As an application on Nielsen fixed point theory, we provide a family of aspherical manifolds without Jiang's Bound Index Property. Moreover, we also give some results on the fixed subgroups of the direct product <span><math><mi>H</mi><mo>×</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> for <em>H</em> a non-elementary torsion-free hyperbolic group.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108028"},"PeriodicalIF":0.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271588","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
A homological approach to chromatic complexity of algebraic K-theory 代数k理论色复杂度的同调方法
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-09 DOI: 10.1016/j.jpaa.2025.108027
Gabriel Angelini-Knoll , J.D. Quigley
{"title":"A homological approach to chromatic complexity of algebraic K-theory","authors":"Gabriel Angelini-Knoll ,&nbsp;J.D. Quigley","doi":"10.1016/j.jpaa.2025.108027","DOIUrl":"10.1016/j.jpaa.2025.108027","url":null,"abstract":"<div><div>The family of Thom spectra <span><math><mi>y</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> interpolates between the sphere spectrum and the mod two Eilenberg–MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum <span><math><mi>y</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> has type <em>n</em>. Using trace methods, we give evidence that algebraic K-theory preserves this chromatic complexity. Our approach sheds light on the chromatic complexity of topological negative cyclic homology and topological peridic cyclic homology, which approximate algebraic K-theory and are of independent interest. Our main contribution is a homological approach that can be applied in great generality, such as to associative ring spectra <em>R</em> without additional structure whose coefficient rings are not completely understood.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108027"},"PeriodicalIF":0.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262695","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
Jones index theorem revisited 琼斯指数定理
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-09 DOI: 10.1016/j.jpaa.2025.108024
Andrey Yu. Glubokov , Igor V. Nikolaev
{"title":"Jones index theorem revisited","authors":"Andrey Yu. Glubokov ,&nbsp;Igor V. Nikolaev","doi":"10.1016/j.jpaa.2025.108024","DOIUrl":"10.1016/j.jpaa.2025.108024","url":null,"abstract":"<div><div>We prove the Jones Index Theorem using the K-theory of a cluster <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra of the Riemann sphere with two boundary components.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108024"},"PeriodicalIF":0.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262798","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
New simple solutions of the Yang–Baxter equation and their permutation groups Yang-Baxter方程的新简单解及其置换群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-06-09 DOI: 10.1016/j.jpaa.2025.108025
F. Cedó , J. Okniński
{"title":"New simple solutions of the Yang–Baxter equation and their permutation groups","authors":"F. Cedó ,&nbsp;J. Okniński","doi":"10.1016/j.jpaa.2025.108025","DOIUrl":"10.1016/j.jpaa.2025.108025","url":null,"abstract":"<div><div>A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang–Baxter equation is constructed. This class complements the class of such solutions constructed in <span><span>[9]</span></span> and together they generalize the class of solutions described in <span><span>[8, Theorem 4.7]</span></span>. Necessary and sufficient conditions are found in order that these new solutions are simple. For a rich subclass of these solutions the structure of their permutation groups, considered as left braces, is determined. In particular, these results answer a question stated in <span><span>[8]</span></span>. In the finite case, all these solutions have square cardinality. A new class of finite simple solutions of non-square cardinality such that their permutation groups are simple left braces is also constructed.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108025"},"PeriodicalIF":0.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271590","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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