Hochschild cohomology on Hopf Galois extensions
type: Item
instance of: scholarly article
title: Hochschild cohomology on Hopf Galois extensions
zbMATH Open document ID: 0838.16008
DOI: 10.1016/0022-4049(95)00101-2
published in: Journal of Pure and Applied Algebra
publication date: 1996-05-30T00:00:00Z
review text: The main result of this interesting article constructs, for a given Hopf Galois extension \(A/B\), spectral sequences connecting the Hochschild cohomologies and homologies of \(A\) and \(B\). As a very special case, this yields the familiar Lyndon-Hochschild-Serre spectral sequences for group extensions and for Lie algebra extensions. Furthermore, the material in this article covers the ring extension \(A_1\subset A\) of a strongly group-graded algebra \(A\) over its identity component \(A_1\) which had previously been studied by the reviewer [Commun. Algebra 20, No. 2, 489-507 (1992; Zbl 0767.16003)].
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 18G60
zbMATH DE Number: 825312
zbMATH Keywords: Hopf Galois extensions
zbMATH Keywords: spectral sequences
zbMATH Keywords: Hochschild cohomologies
zbMATH Keywords: group extensions
zbMATH Keywords: Lie algebra extensions
zbMATH Keywords: ring extensions
zbMATH Keywords: strongly group-graded algebras
author: Dragoş Ştefan
reviewed by: Martin Lorenz
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00101-2
OpenAlex ID: W2065385225
cites work: Crossed products and Galois extensions of Hopf algebras
cites work: Q3708977
cites work: Q3240881
cites work: Semisimple extensions and elements of trace 1
cites work: Hopf extensions of algebras and Maschke type theorems
cites work: Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras
cites work: Separable algebras over commutative rings
cites work: Homology
cites work: Q4011054
cites work: Representation theory of Hopf Galois extensions
cites work: Q5590089
cites work: Q3957087
cites work: On the homology of graded algebras
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description: scientific article; zbMATH DE number 825312