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

Access to Document

10.1016/0021-8693(86)90082-7

Cite this

@article{aca443811b074f3b95290915f5cd42a6,

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",

month = jan,

day = "1",

doi = "10.1016/0021-8693(86)90082-7",

language = "English",

volume = "100",

pages = "363--379",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Hopf algebra actions

AU - Cohen, Miriam

AU - Fishman, Davida

PY - 1986/1/1

Y1 - 1986/1/1

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.

UR - https://www.scopus.com/pages/publications/0000294303

U2 - 10.1016/0021-8693(86)90082-7

DO - 10.1016/0021-8693(86)90082-7

M3 - Article

AN - SCOPUS:0000294303

SN - 0021-8693

VL - 100

SP - 363

EP - 379

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Hopf algebra actions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this