A Galois correspondence for compact group actions on C⁎-algebras

Compact Quantum Group Actions on C*-algebras and Invariant Derivations

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

Let M be a factor with separable predual and G a compact group of automorphisms of M whose action is minimal, i.e. M ′ ∩M = C, where M denotes the G-fixed point subalgebra. Then every intemediate von Neumann algebra M ⊂ N ⊂ M has the form N = M for some closed subgroup H of G. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions...

galois extension for a compact quantum group

The aim of this paper is to introduce the quantum analogues of torsors for a compact quantum group and to investigate their relations with representation theory. Let A be a Hopf algebra over a field k. A theorem of Ulbrich asserts that there is an equivalence of categories between neutral fibre functors on the category of finitedimensional A-comodules and A-Galois extensions of k. We give the c...

On Morita Equivalence of Group Actions on Locally C-algebras

In this paper, we prove that two continuous inverse limit actions α and β of a locally compact group G on the locally C-algebras A and B are strongly Morita equivalent if and only if there is a locally C-algebra C such that A and B appear as two complementary full corners of C and there is a continuous action γ of G on C which leaves A and B invariant such that γ|A = α and γ|B = β. This general...