Journal of Operator Theory

Volume 37, Issue 2, Spring 1997 pp. 311-340.

Characterisations of crossed products by partial actions

Authors: John Quigg (1) and Iain Raeburn (2)
Author institution:(1) Department of Mathematics, Arizona, State University, Tempe, Arizona 85287, U.S.A. E-mail: quigg@math.la.asu.edu
(2) Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, AUSTRALIA. E-mail: iain@frey.newcastle.edu.au

Summary: Partial actions of discrete groups on C*-algebras and the associated crossed products have been studied by Exel and McClanahan. We characterise these crossed products in terms of the spectral subspaces of the dual coaction, generalising and simplifying a theorem of Exel for single partial automorphisms. We then use this characterisation to identify the Cuntz algebras and the Toeplitz algebras of Nica as crossed products by partial actions.

Keywords: Crossed product, partial action, Cuntz algebra.

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