Categorical Landstad duality for actions

Details Categorical Landstad duality for actions Categorical Landstad duality for actions

2006-12-26

arxiv.org/abs/math/0612771v2

Mathematics

Operator Algebras

29 pages. Extensively revised, although essentially the same main results

Scientific paper

We show that the category 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 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.

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