Partial Hopf actions on generalized matrix algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915726910029824 |
|---|---|
| author | Bagio, Dirceu Batista, Eliezer Pinedo, Hector |
| author_facet | Bagio, Dirceu Batista, Eliezer Pinedo, Hector |
| contents | Let $\Bbbk$ be a field, $H$ a Hopf algebra over $\Bbbk$, and $R = (_iM_j)_{1 \leq i,j \leq n}$ a generalized matrix algebra. In this work, we establish necessary and sufficient conditions for $H$ to act partially on $R$. To achieve this, we introduce the concept of an opposite covariant pair and demonstrate that it satisfies a universal property. In the special case where $H = \Bbbk G$ is the group algebra of a group $G$, we recover the conditions given in \cite{BP} for the existence of a unital partial action of $G$ on $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial Hopf actions on generalized matrix algebras Bagio, Dirceu Batista, Eliezer Pinedo, Hector Rings and Algebras Let $\Bbbk$ be a field, $H$ a Hopf algebra over $\Bbbk$, and $R = (_iM_j)_{1 \leq i,j \leq n}$ a generalized matrix algebra. In this work, we establish necessary and sufficient conditions for $H$ to act partially on $R$. To achieve this, we introduce the concept of an opposite covariant pair and demonstrate that it satisfies a universal property. In the special case where $H = \Bbbk G$ is the group algebra of a group $G$, we recover the conditions given in \cite{BP} for the existence of a unital partial action of $G$ on $R$. |
| title | Partial Hopf actions on generalized matrix algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2412.09552 |