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Journal of Functional Analysis 236 (2006) 609–629
www.elsevier.com/locate/jfa
On action of diffeomorphisms of C*-algebras on
derivations
Edward Kissin
Department of Computing, Communications Technology and Mathematics, London Metropolitan University,
166-220 Holloway Road, London N7 8DB, UK
Received 9 January 2006; accepted 13 March 2006
Available online 18 April 2006
Communicated by J. Cuntz
Abstract
In this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show
that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms
generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups
of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers
of derivations.
© 2006 Elsevier Inc. All rights reserved.
Keywords: Derivations; C*-algebras; Automorphisms; Diffeomorphisms
1. Introduction
Extensive development of non-commutative geometry requires elaborating of the theory of the
domains of closed *-derivations of C*-algebras whose properties in many respects are analogous
to the properties of algebras of differentiable functions. In this paper we consider automorphisms
of the domains of derivations and show that they extend to automorphisms of C*-algebras, so we
call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed
*-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define
“bounded” shifts of derivations and the subgroups of the stabilizers of derivations.
E-mail address: e.kissin@londonmet.ac.uk.
0022-1236/$ – see front matter © 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.jfa.2006.03.009