Semisimple Hopf actions on Weyl algebras

2014/09/05 by Cuadra, Juan, Etingof, Pavel, Walton, Chelsea · 2 citations
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1409.1644

Abstract

We study actions of semisimple Hopf algebras H on Weyl algebras A over a field of characteristic zero. We show that the action of H on A must factor through a group algebra; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include reduction modulo a prime number and the study of semisimple cosemisimple Hopf actions on division algebras.

Cited by

• H-Equivariant Morita equivalences of Loewy-graded comodule algebras
• Hopf actions on Poisson algebras

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