arXiv - MATH - Rings and Algebras最新文献_第6页

On the geometry of spaces of filtrations on local rings 论局部环上滤波空间的几何学

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-03 DOI: arxiv-2409.01705

Lu Qi

引用次数: 0

Cup product, Frölicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras 杯积、弗罗里舍-尼延胡斯括号以及与 Hom-Lie 对象相关的派生括号

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-03 DOI: arxiv-2409.01865

Anusuiya Baishya, Apurba Das

引用次数: 0

On the holes in $I^n$ for symmetric bilinear forms in characteristic 2 论特征 2 中对称双线性形式的 $I^n$ 中的洞

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-03 DOI: arxiv-2409.02061

Stephen Scully

{"title":"On the holes in $I^n$ for symmetric bilinear forms in characteristic 2","authors":"Stephen Scully","doi":"arxiv-2409.02061","DOIUrl":"https://doi.org/arxiv-2409.02061","url":null,"abstract":"Let $F$ be a field. Following the resolution of Milnor's conjecture relating\u0000the graded Witt ring of $F$ to its mod-2 Milnor $K$-theory, a major problem in\u0000the theory of symmetric bilinear forms is to understand, for any positive\u0000integer $n$, the low-dimensional part of $I^n(F)$, the $n$th power of the\u0000fundamental ideal in the Witt ring of $F$. In a 2004 paper, Karpenko used\u0000methods from the theory of algebraic cycles to show that if $mathfrak{b}$ is a\u0000non-zero anisotropic symmetric bilinear form of dimension $< 2^{n+1}$\u0000representing an element of $I^n(F)$, then $mathfrak{b}$ has dimension $2^{n+1}\u0000- 2^i$ for some $1 leq i leq n$. When $i = n$, a classical result of Arason\u0000and Pfister says that $mathfrak{b}$ is similar to an $n$-fold Pfister form. At\u0000the next level, it has been conjectured that if $n geq 2$ and $i= n-1$, then\u0000$mathfrak{b}$ is isometric to the tensor product of an $(n-2)$-fold Pfister\u0000form and a $6$-dimensional form of trivial discriminant. This has only been\u0000shown to be true, however, when $n = 2$, or when $n = 3$ and $mathrm{char}(F)\u0000neq 2$ (another result of Pfister). In the present article, we prove the\u0000conjecture for all values of $n$ in the case where $mathrm{char}(F) =2$. In\u0000addition, we give a short and elementary proof of Karpenko's theorem in the\u0000characteristic-2 case, rendering it free from the use of subtle\u0000algebraic-geometric tools. Finally, we consider the question of whether\u0000additional dimension gaps can appear among the anisotropic forms of dimension\u0000$geq 2^{n+1}$ representing an element of $I^n(F)$. When $mathrm{char}(F) neq\u00002$, a result of Vishik asserts that there are no such gaps, but the situation\u0000seems to be less clear when $mathrm{char}(F) = 2$.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A recollement approach to Han's conjecture 韩氏猜想的重补方法

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-02 DOI: arxiv-2409.00945

Ren Wang, Xiaoxiao Xu, Jinbi Zhang, Guodong Zhou

引用次数: 0

(Semi)topological $K$-theory via solidification (通过固化的（半）拓扑 $K$ 理论

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-02 DOI: arxiv-2409.01462

Ko Aoki

引用次数: 0

Bialgebra theory for nearly associative algebras and $LR$-algebras: equivalence, characterization, and $LR$-Yang-Baxter Equation 近关联代数和 $LR$ 代数的代数理论：等价、表征和 $LR$ 扬-巴克斯特方程

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-31 DOI: arxiv-2409.00390

Elisabete Barreiro, Saïd Benayadi, Carla Rizzo

引用次数: 0

Quasi-twilled associative algebras, deformation maps and their governing algebras 准扭曲关联代数、变形映射及其支配代数

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-31 DOI: arxiv-2409.00443

Apurba Das, Ramkrishna Mandal

{"title":"Quasi-twilled associative algebras, deformation maps and their governing algebras","authors":"Apurba Das, Ramkrishna Mandal","doi":"arxiv-2409.00443","DOIUrl":"https://doi.org/arxiv-2409.00443","url":null,"abstract":"A quasi-twilled associative algebra is an associative algebra $mathbb{A}$\u0000whose underlying vector space has a decomposition $mathbb{A} = A oplus B$\u0000such that $B subset mathbb{A}$ is a subalgebra. In the first part of this\u0000paper, we give the Maurer-Cartan characterization and introduce the cohomology\u0000of a quasi-twilled associative algebra. In a quasi-twilled associative algebra $mathbb{A}$, a linear map $D: A\u0000rightarrow B$ is called a strong deformation map if $mathrm{Gr}(D) subset\u0000mathbb{A}$ is a subalgebra. Such a map generalizes associative algebra\u0000homomorphisms, derivations, crossed homomorphisms and the associative analogue\u0000of modified {sf r}-matrices. We introduce the cohomology of a strong\u0000deformation map $D$ unifying the cohomologies of all the operators mentioned\u0000above. We also define the governing algebra for the pair $(mathbb{A}, D)$ to\u0000study simultaneous deformations of both $mathbb{A}$ and $D$. On the other hand, a linear map $r: B rightarrow A$ is called a weak\u0000deformation map if $mathrm{Gr} (r) subset mathbb{A}$ is a subalgebra. Such a\u0000map generalizes relative Rota-Baxter operators of any weight, twisted\u0000Rota-Baxter operators, Reynolds operators, left-averaging operators and\u0000right-averaging operators. Here we define the cohomology and governing algebra\u0000of a weak deformation map $r$ (that unify the cohomologies of all the operators\u0000mentioned above) and also for the pair $(mathbb{A}, r)$ that govern\u0000simultaneous deformations.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Monoids, dynamics and Leavitt path algebras 单体、动力学和勒维路径代数

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-30 DOI: arxiv-2409.00289

Gene Abrams, Roozbeh Hazrat

引用次数: 0

From free idempotent monoids to free multiplicatively idempotent rigs 从自由幂等单体到自由乘法幂等钻机

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-30 DOI: arxiv-2408.17440

Morgan Rogers

引用次数: 0

Wild blocks of type $A$ Hecke algebras are strictly wild A$型Hecke代数的野块是严格野块

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-29 DOI: arxiv-2408.16477

Liron Speyer

引用次数: 0