Tannaka–Kreĭn duality for compact quantum homogeneous spaces. I. General theory

By K. De Commer, Makoto Yamashita. Theory and Applications of Categories, 2012

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An ergodic action of a compact quantum group G on an operator algebra A can be interpreted as a quantum homogeneous space for G. Such an action gives rise to the category of finite equivariant Hilbert modules over A, which has a module structure over the tensor category Rep(G) of finite dimensional representations of G. We show that there is a one-to-one correspondence between the quantum G-homogeneous spaces up to equivariant Morita equivalence, and indecomposable module C*-categories over Rep(G) up to natural equivalence. This gives a global approach to the duality theory for ergodic actions as developed by C. Pinzari and J. Roberts.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7332776c628dd786dbe1329b6d52758240a3f06c