Hopf algebra actions

Miriam Cohen, Davida Fishman

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

Finite groups acting on rings by automorphisms, and group-graded rings are instances of Hopf algebras H acting on H-module algebras A. We study such actions. Let AH = {a ε{lunate} A|h · a = ε(h) a, all h ε{lunate} H}, the ring of H-invariants, and form the smash product A # H. We study the ring extensions AH ⊂A ⊂A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [AH, A, A, A # H] and use these to get connections between the various rings.

Original languageEnglish
Pages (from-to)363-379
Number of pages17
JournalJournal of Algebra
Volume100
Issue number2
DOIs
StatePublished - 1 Jan 1986

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