Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.06825 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908341228273664 |
|---|---|
| author | Rasmussen, Anna Rodriguez |
| author_facet | Rasmussen, Anna Rodriguez |
| contents | Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and on the corresponding skew group algebra. Assuming a natural compatibility condition on the partial order, we show that the skew group algebra is quasi-hereditary if and only if the original algebra is. Moreover, we show that in this setting an exact Borel subalgebra of the original algebra which is invariant as a set under the group action gives rise to an exact Borel subalgebra of the skew group algebra, and that under this construction, properties such as normality and regularity of the exact Borel subalgebra are preserved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06825 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-Hereditary Skew Group Algebras Rasmussen, Anna Rodriguez Representation Theory Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and on the corresponding skew group algebra. Assuming a natural compatibility condition on the partial order, we show that the skew group algebra is quasi-hereditary if and only if the original algebra is. Moreover, we show that in this setting an exact Borel subalgebra of the original algebra which is invariant as a set under the group action gives rise to an exact Borel subalgebra of the skew group algebra, and that under this construction, properties such as normality and regularity of the exact Borel subalgebra are preserved. |
| title | Quasi-Hereditary Skew Group Algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2305.06825 |