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arXiv · 2409.17890

Actions of Taft Algebras on Noetherian Down-Up Algebras

Simon Crawford·Jason Gaddis·Robert Won
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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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Simon Crawford, Jason Gaddis, Robert Won. 2024-09-26. Actions of Taft Algebras on Noetherian Down-Up Algebras. https://arxiv.org/abs/2409.17890

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