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- Title
Non-commutative ambits and equivariant compactifications.
- Authors
Chirvasitu, Alexandru
- Abstract
We prove that an action ρ:A→M(C0(G)⊗A) of a locally compact quantum group on a C∗-algebra has a universal equivariant compactification, and prove a number of other category-theoretic results on G-equivariant compactifications: that the categories compactifications of ρ and A respectively are locally presentable (hence complete and cocomplete), that the forgetful functor between them is a colimit-creating left adjoint, and that epimorphisms therein are surjective and injections are regular monomorphisms. When G is regular coamenable we also show that the forgetful functor from unital G-C∗-algebras to unital C∗-algebras creates finite limits and is comonadic, and that the monomorphisms in the former category are injective.
- Subjects
QUANTUM groups; COMPACT groups; C*-algebras
- Publication
Journal of Noncommutative Geometry, 2024, Vol 18, Issue 2, p567
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/536