Actions of Taft Algebras on Noetherian Down-Up Algebras

2024/09/26 by Crawford, Simon, Gaddis, Jason, Won, Robert · 1 citation
#16E65 #16T05 #16W22 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2409.17890

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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