A Galois correspondence for compact quantum group actions

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...

Quantum Galois theory for compact Lie groups

We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.

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

Equivariant Periodicity for Compact Group Actions

Probably the most basic structural phenomenon of high dimensional topology is Siebenmann’s periodicity theorem [3] (as amended by Nicas [5]), which asserts that the manifolds homotopy equivalent to M are in a one-to-one correspondence with (a subset of, because of nonresolvable honology manifolds [1]) those homotopy equivalent to M×D. The main goal of this paper is to show the following extensi...