Non-commutative ambits and equivariant compactifications

  • Alexandru Chirvasitu

    University at Buffalo, USA
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We prove that an action of a locally compact quantum group on a -algebra has a universal equivariant compactification and prove a number of other category-theoretic results on -equivariant compactifications: that the categories compactifications of and , 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 is regular, coamenable we also show that the forgetful functor from unital --algebras to unital -algebras creates finite limits and is comonadic and that the monomorphisms in the former category are injective.

Cite this article

Alexandru Chirvasitu, Non-commutative ambits and equivariant compactifications. J. Noncommut. Geom. 18 (2024), no. 2, pp. 567–603

DOI 10.4171/JNCG/536