Computing the Brauer group of graded Azumaya algebras from its subgroups
type: Item
instance of: scholarly article
title: Computing the Brauer group of graded Azumaya algebras from its subgroups
zbMATH Open document ID: 0589.16002
DOI: 10.1016/0021-8693(86)90198-5
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: For a connected commutative ring R with identity and G a finite abelian group, \textit{F. W. Long} [Proc. Lond. Math. Soc., III. Ser. 29, 237-256 (1974; Zbl 0294.13003)] introduced a generalized Brauer group of algebras with a G-grading upon which G acts as a group of grade-preserving automorphisms. The author investigates the structure of BD(R,G) for noncyclic G. The cyclic case was previously studied by several authors. A sample result which the author proves is the following. She introduces a subgroup \({\mathcal A}\) of central algebras with trivial action cocycle and shows that \({\mathcal A}\cong BC(R,G)\times BT(R,G)\); where BC(R,G) is the subgroup of classes for which a representative has trivial action, and BT(R,G) is a subgroup isomorphic to Aut(G).
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 14F22
zbMATH DE Number: 3946371
zbMATH Keywords: graded Azumaya algebras
zbMATH Keywords: generalized Brauer group of algebras
zbMATH Keywords: group of grade-preserving automorphisms
zbMATH Keywords: central algebras
author: Margaret Beattie
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90198-5
OpenAlex ID: W2053689153
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description: scientific article; zbMATH DE number 3946371