arXiv 1007.24382010-07math.OAmath-phmath.MPmath.QA

On a certain approach to quantum homogeneous spaces

Pawel Kasprzak

备注：: A gap in the proof of Theorem 5.1 was removed. New proof is shorter and simpler

英文摘要：

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 a homogeneous spaces. On the quantum level our definition goes beyond the quotient case. It provides 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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