On Solvability of Automorphism Groups of Commutative Algebras
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909978824015872 |
|---|---|
| author | Das, Dibyendu |
| author_facet | Das, Dibyendu |
| contents | Let $A$ be a finite-dimensional commutative associative algebra with unity over an algebraically closed field $\mathbb{K}$. The purpose of the paper is to study the solvability of $G_A$, where $G_A$ is the identity component of $\text{Aut}_\mathbb{K}(A)$. Inspired by Pollack's work, Saorín and Asensio have started this study for a commutative associative algebra $A$ when $\text{dim}(R/R^2)=2$, where $R$ is the Jacobson radical of $A$. In this paper, we give new sufficient conditions on $A$ so that $G_A$ is solvable without any restriction on $\text{dim}(R/R^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Solvability of Automorphism Groups of Commutative Algebras Das, Dibyendu Group Theory Commutative Algebra 20Gxx, 16Gxx Let $A$ be a finite-dimensional commutative associative algebra with unity over an algebraically closed field $\mathbb{K}$. The purpose of the paper is to study the solvability of $G_A$, where $G_A$ is the identity component of $\text{Aut}_\mathbb{K}(A)$. Inspired by Pollack's work, Saorín and Asensio have started this study for a commutative associative algebra $A$ when $\text{dim}(R/R^2)=2$, where $R$ is the Jacobson radical of $A$. In this paper, we give new sufficient conditions on $A$ so that $G_A$ is solvable without any restriction on $\text{dim}(R/R^2)$. |
| title | On Solvability of Automorphism Groups of Commutative Algebras |
| topic | Group Theory Commutative Algebra 20Gxx, 16Gxx |
| url | https://arxiv.org/abs/2512.24364 |