On a certain approach to quantum homogeneous spaces

Details On a certain approach to quantum homogeneous spaces On a certain approach to quantum homogeneous spaces

2010-07-14

arxiv.org/abs/1007.2438v5

Mathematics

Operator Algebras

Several typos were corrected. A mistake in the proof of Theorem 5.1 was corrected. To be published in Communications in Mathem

Scientific paper

We propose a definition of a quantum homogeneous space of a locally compact quantum group. We show that classically it reduces to the notion of homogeneous spaces, giving rise to an operator algebraic characterization of the transitive group actions. On the quantum level our definition goes beyond the quotient case providing a framework which, besides the Vaes' quotient of a locally compact quantum group by its closed quantum subgroup (our main motivation) is also compatible with, generically non-quotient, quantum homogeneous spaces of a compact quantum group studied by P. Podles as well as the Rieffel deformation of G-homogeneous spaces. Finally, our definition rules out the paradoxical examples of the non-compact quantum homogeneous spaces of a compact quantum group.

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