1. Categorical Landstad duality for actions
- Author
-
John Quigg and Steven Kaliszewski
- Subjects
Discrete mathematics ,Pure mathematics ,Fiber functor ,Functor ,Comma category ,Mathematics::Operator Algebras ,General Mathematics ,46L55 (Primary) ,46M15, 18A25 (Secondary) ,Mathematics - Operator Algebras ,Concrete category ,Locally compact group ,Closed category ,Mathematics::Quantum Algebra ,Mathematics::Category Theory ,FOS: Mathematics ,Universal property ,Homomorphism ,Operator Algebras (math.OA) ,Mathematics - Abstract
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., 29 pages. Extensively revised, although essentially the same main results
- Published
- 2009