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Abelian ideals and the variety of Lagrangian subalgebras 阿贝尔理想与拉格朗日子代数的多样性
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-30 DOI: 10.1016/j.jpaa.2024.107813
Sam Evens , Yu Li
{"title":"Abelian ideals and the variety of Lagrangian subalgebras","authors":"Sam Evens ,&nbsp;Yu Li","doi":"10.1016/j.jpaa.2024.107813","DOIUrl":"10.1016/j.jpaa.2024.107813","url":null,"abstract":"<div><div>For a semisimple algebraic group <em>G</em> of adjoint type with Lie algebra <span><math><mi>g</mi></math></span> over the complex numbers, we establish a bijection between the set of closed orbits of the group <span><math><mi>G</mi><mo>⋉</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> acting on the variety of Lagrangian subalgebras of <span><math><mi>g</mi><mo>⋉</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> and the set of abelian ideals of a fixed Borel subalgebra of <span><math><mi>g</mi></math></span>. In particular, the number of such orbits equals <span><math><msup><mrow><mn>2</mn></mrow><mrow><mtext>rk</mtext><mi>g</mi></mrow></msup></math></span> by Peterson's theorem on abelian ideals.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425562","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
Decomposing tensor spaces via path signatures 通过路径签名分解张量空间
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-27 DOI: 10.1016/j.jpaa.2024.107807
Carlos Améndola , Francesco Galuppi , Ángel David Ríos Ortiz , Pierpaola Santarsiero , Tim Seynnaeve
{"title":"Decomposing tensor spaces via path signatures","authors":"Carlos Améndola ,&nbsp;Francesco Galuppi ,&nbsp;Ángel David Ríos Ortiz ,&nbsp;Pierpaola Santarsiero ,&nbsp;Tim Seynnaeve","doi":"10.1016/j.jpaa.2024.107807","DOIUrl":"10.1016/j.jpaa.2024.107807","url":null,"abstract":"<div><div>The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety induces a natural decomposition of the tensor space via representation theory, and connect this to the study of path invariants. We also reveal certain constraints that apply to the rank and symmetry of a signature tensor.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425561","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}
引用次数: 0
A note on the Archimedean Positivstellensatz in real algebraic geometry 关于实代数几何中阿基米德正定定理的说明
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-27 DOI: 10.1016/j.jpaa.2024.107811
Konrad Schmüdgen
{"title":"A note on the Archimedean Positivstellensatz in real algebraic geometry","authors":"Konrad Schmüdgen","doi":"10.1016/j.jpaa.2024.107811","DOIUrl":"10.1016/j.jpaa.2024.107811","url":null,"abstract":"<div><div>A variant of the Archimedean Positivstellensatz is proved which is based on Archimedean semirings or quadratic modules of generating subalgebras. It allows one to obtain representations of strictly positive polynomials on compact semi-algebraic sets by means of smaller sets of squares or polynomials. A large number of examples is developed in detail.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425551","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}
引用次数: 0
Geproci sets on skew lines in P3 with two transversals P3 斜线上有两个横线的格普罗集
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-27 DOI: 10.1016/j.jpaa.2024.107809
Luca Chiantini , Pietro De Poi , Łucja Farnik , Giuseppe Favacchio , Brian Harbourne , Giovanna Ilardi , Juan Migliore , Tomasz Szemberg , Justyna Szpond
{"title":"Geproci sets on skew lines in P3 with two transversals","authors":"Luca Chiantini ,&nbsp;Pietro De Poi ,&nbsp;Łucja Farnik ,&nbsp;Giuseppe Favacchio ,&nbsp;Brian Harbourne ,&nbsp;Giovanna Ilardi ,&nbsp;Juan Migliore ,&nbsp;Tomasz Szemberg ,&nbsp;Justyna Szpond","doi":"10.1016/j.jpaa.2024.107809","DOIUrl":"10.1016/j.jpaa.2024.107809","url":null,"abstract":"<div><div>The purpose of this work is to pursue classification of geproci sets. Specifically we classify <span><math><mo>[</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>]</mo></math></span>-geproci sets <em>Z</em> which consist of <span><math><mi>m</mi><mo>=</mo><mn>4</mn></math></span> points on each of <em>n</em> skew lines, assuming the skew lines have two transversals in common. We show in this case that <span><math><mi>n</mi><mo>≤</mo><mn>6</mn></math></span>. Moreover we show that all geproci sets of this type and with no points on the transversals are contained in the <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> configuration. We conjecture that a similar result is true for an arbitrary number <em>m</em> of points on each skew line, replacing containment in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> by containment in a half grid obtained by the so-called <em>standard construction</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425558","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}
引用次数: 0
Diagonal tensor algebra and naïve liftings 对角张量代数和天真提升
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-27 DOI: 10.1016/j.jpaa.2024.107808
Saeed Nasseh , Maiko Ono , Yuji Yoshino
{"title":"Diagonal tensor algebra and naïve liftings","authors":"Saeed Nasseh ,&nbsp;Maiko Ono ,&nbsp;Yuji Yoshino","doi":"10.1016/j.jpaa.2024.107808","DOIUrl":"10.1016/j.jpaa.2024.107808","url":null,"abstract":"<div><div>The notion of naïve lifting of differential graded (DG) modules along certain DG algebra extensions was introduced by the authors for the purpose of studying problems in homological commutative algebra that involve self-vanishing of Ext. Our goal in this paper is to deeply study naïve lifting property using the diagonal tensor algebra. Our main result provides several characterizations of naïve liftability of DG modules under certain Ext vanishing conditions. As an application, we affirmatively answer a question posed by the authors regarding a specific characterization of naïve liftability.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533599","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
The May filtration on THH and faithfully flat descent THH 上的五月过滤和忠实的平缓下降
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-26 DOI: 10.1016/j.jpaa.2024.107806
Liam Keenan
{"title":"The May filtration on THH and faithfully flat descent","authors":"Liam Keenan","doi":"10.1016/j.jpaa.2024.107806","DOIUrl":"10.1016/j.jpaa.2024.107806","url":null,"abstract":"<div><div>In this article, we study descent properties of topological Hochschild homology and topological cyclic homology. In particular, we verify that both of these invariants satisfy faithfully flat descent and 1-connective descent for connective <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-ring spectra. This generalizes a result of Bhatt–Morrow–Scholze from <span><span>[6]</span></span> and a result of Dundas–Rognes from <span><span>[11]</span></span>, respectively. Along the way, we develop some basic theory for cobar constructions and give an alternative presentation of the May filtration on topological Hochschild homology, originally due to Angelini-Knoll–Salch <span><span>[3]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425559","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
Examples and cofibrant generation of effective Kan fibrations 有效 Kan 纤维的实例和共纤维生成
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-26 DOI: 10.1016/j.jpaa.2024.107812
Benno van den Berg , Freek Geerligs
{"title":"Examples and cofibrant generation of effective Kan fibrations","authors":"Benno van den Berg ,&nbsp;Freek Geerligs","doi":"10.1016/j.jpaa.2024.107812","DOIUrl":"10.1016/j.jpaa.2024.107812","url":null,"abstract":"<div><div>We will make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that simplicial Malcev algebras are effective Kan complexes and that the effective Kan fibrations can be seen as the right class in an algebraic weak factorization system. In addition, we will introduce two strengthenings of the notion of an effective Kan fibration, the symmetric effective and degenerate-preferring Kan fibrations, and show that the previous results hold for these strengthenings as well.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425560","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}
引用次数: 0
Jacobian varieties with group algebra decomposition not affordable by Prym varieties 具有群代数分解的雅各布品种不是普莱姆品种所能负担得起的
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-13 DOI: 10.1016/j.jpaa.2024.107803
Benjamín M. Moraga
{"title":"Jacobian varieties with group algebra decomposition not affordable by Prym varieties","authors":"Benjamín M. Moraga","doi":"10.1016/j.jpaa.2024.107803","DOIUrl":"10.1016/j.jpaa.2024.107803","url":null,"abstract":"<div><div>The action of a finite group <em>G</em> on a compact Riemann surface <em>X</em> naturally induces another action of <em>G</em> on its Jacobian variety <span><math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. In many cases, each component of the group algebra decomposition of <span><math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is isogenous to a Prym varieties of an intermediate covering of the Galois covering <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi><mo>/</mo><mi>G</mi></math></span>; in such a case, we say that the group algebra decomposition is affordable by Prym varieties. In this article, we present an infinite family of groups that act on Riemann surfaces in a manner that the group algebra decomposition of <span><math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is not affordable by Prym varieties; namely, affine groups <span><math><mi>Aff</mi><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span> with some exceptions: <span><math><mi>q</mi><mo>=</mo><mn>2</mn></math></span>, <span><math><mi>q</mi><mo>=</mo><mn>9</mn></math></span>, <em>q</em> a Fermat prime, <span><math><mi>q</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn></math></span> a Mersenne prime and some particular cases when <span><math><mi>X</mi><mo>/</mo><mi>G</mi></math></span> has genus 0 or 1. In each one of this exceptional cases, we give the group algebra decomposition of <span><math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> by Prym varieties.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315895","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 transcendental lattices of Hyper-Kähler manifolds 论超凯勒流形的超越网格
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-12 DOI: 10.1016/j.jpaa.2024.107805
Benedetta Piroddi , Ángel David Ríos Ortiz
{"title":"On the transcendental lattices of Hyper-Kähler manifolds","authors":"Benedetta Piroddi ,&nbsp;Ángel David Ríos Ortiz","doi":"10.1016/j.jpaa.2024.107805","DOIUrl":"10.1016/j.jpaa.2024.107805","url":null,"abstract":"<div><p>We introduce the notion of a Hyper-Kähler manifold <em>X</em> induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of Hyper-Kähler manifolds studying those that are induced by a K3 or abelian surface (that is, induced by the Hodge structure of their transcendental lattice), giving lattice-theoretic criteria to decide whether or not they are birational to a moduli space of sheaves over said surface. We highlight the different behaviors we find for the particular class of Hyper-Kähler manifolds of O'Grady type.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924002020/pdfft?md5=edd17e74a859b78f7d2ca46a3aecaa1f&pid=1-s2.0-S0022404924002020-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142237324","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}
引用次数: 0
Some remarks on spin-orbits of unit vectors 关于单位矢量自旋轨道的一些评论
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107802
Tariq Syed
{"title":"Some remarks on spin-orbits of unit vectors","authors":"Tariq Syed","doi":"10.1016/j.jpaa.2024.107802","DOIUrl":"10.1016/j.jpaa.2024.107802","url":null,"abstract":"<div><p>For <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> and a commutative ring <em>R</em> with <span><math><mn>2</mn><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>×</mo></mrow></msup></math></span>, the group <span><math><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> acts on the set <span><math><mi>U</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> of unimodular vectors of length <em>n</em> and <span><math><mi>S</mi><mi>p</mi><mi>i</mi><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> acts on the set of unit vectors <span><math><msub><mrow><mi>U</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. We give an example of a ring for which the comparison map <span><math><mi>U</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>/</mo><mi>S</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>→</mo><msub><mrow><mi>U</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>/</mo><mi>S</mi><mi>p</mi><mi>i</mi><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> fails to be bijective.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001993/pdfft?md5=92a252c768ddb3132dc1cf4aa6995e84&pid=1-s2.0-S0022404924001993-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173339","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}
引用次数: 0
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