Categorical Landstad duality for actions

2006/12/26 by S. Kaliszewski, John Quigg, Kaliszewski, S. +1 · 3 citations
Mathematics · Medicine · #18A25 (Secondary) #46L55 (Primary) #46M15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0612771

openalex publication_date 2006/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On groupoid-graded C*-algebras and equivalent subcategories linked via monads and comonads
• Proper actions, fixed-point algebras and naturality in nonabelian duality
• Naturality of Rieffel's Morita equivalence for proper actions

Related

• Three versions of categorical crossed-product duality
• Landstad's characterization for full crossed products
• Crossed products for actions of crossed modules on C*-algebras
• Full and reduced coactions of locally compact groups on C*-algebras
• Proper actions, fixed-point algebras and naturality in nonabelian duality