Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-23T06:40:02.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphisms of homogeneous C*-algebras

Published online by Cambridge University Press:  17 April 2009

Klaus Thomsen
Klaus Thomsen
Affiliation:
Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK – Aarhus C, Denmark.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a homogeneous C*-algebra we identify the quotient of the automorphism group by the locally unitary automorphisms as a subgroup of the homeomorphisms of the spectrum. We sharpen a known criterion on the spectrum that ensures that all locally unitary automorphisms of the algebra are inner.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 145 - 154
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Baum, P.F. and Browder, W., “The cohomology of quotients of classical groups”, Topology, 3 (1965), 305–336.CrossRefGoogle Scholar
[2]Fell, J.M.G., “The structure of algebras of operator fields”, Acta Math., 106 (1961), 233–280.CrossRefGoogle Scholar
[3]Fell, J.M.G., “An extension of Mackey's method to Banach *-algebraic bundles”, Mem. Amer. Math. Soc., 90 (1969.Google Scholar
[4]Hirzebruch, F., Topological Methods in Algebraic Geometry, (Springer Verlag, Berlin-Heidelberg-N.Y., 1966).Google Scholar
[5]Kadison, R.V. and Ringrose, J.R., “Derivations and automorphisms of operator algebras”, Comm. Math. Phys., 4 (1967), 32–63.CrossRefGoogle Scholar
[6]Knus, M.A., “Aleèbres d'Azumaya et modules projectifs”, Comment Math. Helv., 45 (1970), 372–383.CrossRefGoogle Scholar
[7]Phillips, J. and Raeburn, Iain, “Automorphisms of C*-algebras and second Cech Cohomology”, Indiana Univ. Math. J., 29 (1980), 799–822.CrossRefGoogle Scholar
[8]Phillips, J. and Raeburn, Iain, “Crossed products by locally unitary automorphism groups and principal bundles”, J. Operator Theory, 11 (1984), 215–241.Google Scholar
[9]Russell, M.J., “Automorphisms and derivations of continuous trace C*-algebras”, J. London Math. Soc., (2)22 (1980), 139–145.CrossRefGoogle Scholar