IUMJ

Title: Categorical Landstad duality for actions

Authors: S. Kaliszewski and John Quigg

Issue: Volume 58 (2009), Issue 1, 415-442

Abstract:

We show that the category $\mathcal{A}(G)$ of actions of a locally compact group $G$ on $C^{*}$-algebras (with equivariant nondegenerate $*$-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of $G$ under the comultiplication $(C^{*}(G),\delta_G)$; and also that $\mathcal{A}(G)$ is equivalent, via a reduced-crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those $C^{*}$-algebras which are isomorphic to crossed products by $G$ as precisely those which form part of an object in the appropriate comma category.