Hopf algebra actions

Miriam Cohen; Davida Fishman

doi:10.1016/0021-8693(86)90082-7

Hopf algebra actions

Miriam Cohen, Davida Fishman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

83 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 A^H = {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 A^H ⊂A ⊂A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [A^H, A, A, A # H] and use these to get connections between the various rings.

Original language	English
Pages (from-to)	363-379
Number of pages	17
Journal	Journal of Algebra
Volume	100
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(86)90082-7
State	Published - 1 Jan 1986

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0021-8693(86)90082-7

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title = "Hopf algebra actions",

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.",

author = "Miriam Cohen and Davida Fishman",

year = "1986",

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N2 - 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.

AB - 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.

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Hopf algebra actions

Abstract

ASJC Scopus subject areas

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