Actions of Taft Algebras on Noetherian Down-Up Algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909327186460672 |
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| author | Crawford, Simon Gaddis, Jason Won, Robert |
| author_facet | Crawford, Simon Gaddis, Jason Won, Robert |
| contents | We consider actions of Taft algebras on noetherian graded down-up algebras. We classify all such actions and determine properties of the corresponding invariant rings $A^T$. We identify precisely when $A^T$ is commutative, when it is Artin-Schelter regular, and give sufficient conditions for it to be Artin-Schelter Gorenstein. Our results show that many results and conjectures in the literature concerning actions of semisimple Hopf algebras on Artin-Schelter regular algebras can fail when the semisimple hypothesis is omitted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Actions of Taft Algebras on Noetherian Down-Up Algebras Crawford, Simon Gaddis, Jason Won, Robert Rings and Algebras 16E65, 16T05, 16W22, 16W50 We consider actions of Taft algebras on noetherian graded down-up algebras. We classify all such actions and determine properties of the corresponding invariant rings $A^T$. We identify precisely when $A^T$ is commutative, when it is Artin-Schelter regular, and give sufficient conditions for it to be Artin-Schelter Gorenstein. Our results show that many results and conjectures in the literature concerning actions of semisimple Hopf algebras on Artin-Schelter regular algebras can fail when the semisimple hypothesis is omitted. |
| title | Actions of Taft Algebras on Noetherian Down-Up Algebras |
| topic | Rings and Algebras 16E65, 16T05, 16W22, 16W50 |
| url | https://arxiv.org/abs/2409.17890 |