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C*-crossed products by partial actions and actions of inverse semigroups

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Nándor Sieben
Nándor Sieben
Affiliation:
Department of Mathematics Arizona State UniversityTempe AZ 85287-1804, USA
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Abstract

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The recently developed theory of partial actions of discrete groups on C*-algebras is extended. A related concept of actions of inverse semigroups on C*-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 1 , August 1997 , pp. 32 - 46
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Duncan, J. and Paterson, A. L. T., ‘C*-algebras of inverse semigroups’, Proc. Edinburgh Math. Soc. 28 (1985), 41–58.CrossRefGoogle Scholar
[2]Duncan, J. and Paterson, A. L. T., ‘C*-algebras of Clifford semigroups’, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 129–145.CrossRefGoogle Scholar
[3]Exel, R., ‘Circle actions on C*-algebras, partial automorphisms and a generalized Pimsner-Voiculescu exact sequence’, J. Funct. Anal. 122 (1994), 361–401.CrossRefGoogle Scholar
[4]Howie, J. M., An introduction to semigroup theory (Academic press, London, 1976).Google Scholar
[5]McClanahan, K., ‘K-theory for partial crossed products by discrete groups’, J. Funct. Anal. 130 (1995), 77–117.CrossRefGoogle Scholar
[6]Paterson, A. L. T., ‘Weak containment and Clifford semigroups’, Proc. Roy. Soc. Edinburgh Sect. A 81 (1978), 23–30.Google Scholar
[7]Paterson, A. L. T., ‘Inverse semigroups, groupoids and a problem of J. Renault’, (Birkhäuser, Boston, 1993) pp. 11.Google Scholar
[8]Renault, J. N., ‘A groupoid approach to C*-algebras’, in: Lecture Notes in Math. 793 (Springer, New York, 1980).Google Scholar
[9]Renault, J. N., ‘Représentation des produits croisés d'algèbres de groupoides’, J. Operator Theory 18 (1987), 67–97.Google Scholar
[10]Wordingham, J. R., ‘The left regular *-representation of an inverse semigroup’, Proc. Amer. Math. Soc. 86 (1982), 55–58.Google Scholar