Actions of Taft Algebras on Noetherian Down-Up Algebras

Autor:	Crawford, Simon, Gaddis, Jason, Won, Robert
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras 16E65 16T05 16W22 16W50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.17890 Zobrazit plný text záznamu View this record from Arxiv