Ozone groups of Artin--Schelter regular algebras satisfying a polynomial identity
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910639607250944 |
|---|---|
| author | Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. |
| author_facet | Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. |
| contents | We study the ozone group of noetherian Artin--Schelter regular algebras satisfying a polynomial identity (or PI for short). The ozone group was shown in previous work by the authors to be an important invariant in the study of PI skew polynomial rings and their centers. In this paper, we show that skew polynomial rings are in fact characterized as those algebras with maximal rank ozone groups. We also classify those with trivial ozone groups, which must necessarily be Calabi--Yau. This class includes most three-dimensional PI Sklyanin algebras. Further examples and applications are given, including applications to the Zariski Cancellation Problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ozone groups of Artin--Schelter regular algebras satisfying a polynomial identity Chan, Kenneth Gaddis, Jason Won, Robert Zhang, James J. Rings and Algebras We study the ozone group of noetherian Artin--Schelter regular algebras satisfying a polynomial identity (or PI for short). The ozone group was shown in previous work by the authors to be an important invariant in the study of PI skew polynomial rings and their centers. In this paper, we show that skew polynomial rings are in fact characterized as those algebras with maximal rank ozone groups. We also classify those with trivial ozone groups, which must necessarily be Calabi--Yau. This class includes most three-dimensional PI Sklyanin algebras. Further examples and applications are given, including applications to the Zariski Cancellation Problem. |
| title | Ozone groups of Artin--Schelter regular algebras satisfying a polynomial identity |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2312.13014 |