A remark on compact automorphism groups of \(C^*\)-algebras
type: Item
instance of: scholarly article
title: A remark on compact automorphism groups of \(C^*\)-algebras
zbMATH Open document ID: 0589.46052
DOI: 10.1016/0022-1236(86)90081-9
author: Sergio Doplicher
author: John E. Roberts
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: The following results is proved. A \(C^*\)-system over a compact group whose fixed-point algebra has trivial centre and relative commutant coinciding with the centre of the full algebra is obtained canonically by inducing up from a \(C^*\)-system over a closed subgroup which now has trivial relative commutant. This result is used in an essential way to determine the compact Lie group associated with certain endomorphisms of \(C^*\)-algebras, in the course of the development of a new duality theory for compact groups in terms of \(C^*\)-algebras [cf. by the same authors: Bull. Am. Math. Soc., New Ser. 11, 333-338 (1984; Zbl 0561.46029); ''Duals of compact groups realized in the Cuntz algebras and their actions on \(C^*\)-algebras'', J. Funct. Anal., to appear; Proceedings of the Marseille Conference on Mathematical Physics, July 1986, World Scientific P. Co., to appear].
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 43A40
Mathematics Subject Classification ID: 22D35
zbMATH DE Number: 3946927
zbMATH Keywords: \(C^*\)-system over a compact group
zbMATH Keywords: fixed-point algebra
zbMATH Keywords: trivial centre
zbMATH Keywords: relative commutant
zbMATH Keywords: compact Lie group
zbMATH Keywords: endomorphisms of \(C^*\)-algebras
zbMATH Keywords: new duality theory for compact groups in terms of \(C^*\)-algebras
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90081-9
OpenAlex ID: W2005297381
cites work: Compact Lie groups associated with endomorphisms of 𝐶*-algebras
cites work: Primitive ideals in enveloping algebras
cites work: Applications of the Connes spectrum to C*-dynamical systems. III
description: scientific article; zbMATH DE number 3946927