An equivariant Brauer semigroup and the symmetric imprimitivity theorem

Authors:
Astrid an Huef, Iain Raeburn and Dana P. Williams

Journal:
Trans. Amer. Math. Soc. **352** (2000), 4759-4787

MSC (2000):
Primary 46L05, 46L35

DOI:
https://doi.org/10.1090/S0002-9947-00-02618-0

Published electronically:
June 14, 2000

MathSciNet review:
1709774

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is a second countable locally compact transformation group. We let denote the set of Morita equivalence classes of separable dynamical systems where is a -algebra and is compatible with the given -action on . We prove that is a commutative semigroup with identity with respect to the binary operation for an appropriately defined balanced tensor product on -algebras. If and act freely and properly on the left and right of a space , then we prove that and are isomorphic as semigroups. If the isomorphism maps the class of to the class of , then is Morita equivalent to .

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Additional Information

**Astrid an Huef**

Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551

Address at time of publication:
Department of Mathematics, University of Denver, Denver, Colorado 80208

Email:
astrid@cs.du.edu

**Iain Raeburn**

Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, New South Wales 2308, Australia

Email:
iain@math.newcastle.edu.au

**Dana P. Williams**

Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551

Email:
dana.williams@dartmouth.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02618-0

Received by editor(s):
November 25, 1998

Published electronically:
June 14, 2000

Article copyright:
© Copyright 2000
American Mathematical Society