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Categorical Landstad duality for actions
- Source :
- Indiana University Mathematics Journal. 58:415-442
- Publication Year :
- 2009
- Publisher :
- Indiana University Mathematics Journal, 2009.
-
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.<br />29 pages. Extensively revised, although essentially the same main results
- 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
Subjects
Details
- ISSN :
- 00222518
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Indiana University Mathematics Journal
- Accession number :
- edsair.doi.dedup.....f62e12672fa1471d5af4f167bca9ce3e