Actions of Taft Algebras on Noetherian Down-Up Algebras

Jason Gaddis; Robert Won; Simon Crawford

Actions of Taft Algebras on Noetherian Down-Up Algebras

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arxiv 2409.17890 v1 pith:3CTYGBJM submitted 2024-09-26 math.RA

Simon Crawford , Jason Gaddis , Robert Won This is my paper

classification math.RA

keywords algebrasactionsartin-schelterwhendown-upnoetherianregularresults

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abstract

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.

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