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Characterisations of crossed products by partial actions. (English) Zbl 0890.46048
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.

##### MSC:
 46L55 Noncommutative dynamical systems