Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.03057 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915227662024704 |
|---|---|
| author | Rogalski, Daniel Won, Robert Zhang, James J. |
| author_facet | Rogalski, Daniel Won, Robert Zhang, James J. |
| contents | We introduce the notion of a homological integral for an infinite-dimensional weak Hopf algebra and use the homological integral to prove several structure theorems. For example, we prove that the Artin--Schelter property and the Van den Bergh condition are equivalent for a noetherian weak Hopf algebra, and that the antipode is automatically invertible in this case. We also prove a decomposition theorem that states that any weak Hopf algebra finite over an affine center is a direct sum of Artin--Schelter Gorenstein, Cohen--Macaulay, GK dimension homogeneous weak Hopf algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological Integrals for Weak Hopf Algebras Rogalski, Daniel Won, Robert Zhang, James J. Quantum Algebra Rings and Algebras 16E10, 16T99, 18D99 We introduce the notion of a homological integral for an infinite-dimensional weak Hopf algebra and use the homological integral to prove several structure theorems. For example, we prove that the Artin--Schelter property and the Van den Bergh condition are equivalent for a noetherian weak Hopf algebra, and that the antipode is automatically invertible in this case. We also prove a decomposition theorem that states that any weak Hopf algebra finite over an affine center is a direct sum of Artin--Schelter Gorenstein, Cohen--Macaulay, GK dimension homogeneous weak Hopf algebras. |
| title | Homological Integrals for Weak Hopf Algebras |
| topic | Quantum Algebra Rings and Algebras 16E10, 16T99, 18D99 |
| url | https://arxiv.org/abs/2504.03057 |