Equivariant comparison of quantum homogeneous spaces

Details Equivariant comparison of quantum homogeneous spaces Equivariant comparison of quantum homogeneous spaces

2011-09-14

arxiv.org/abs/1109.2991v1

Mathematics

Operator Algebras

15 pages

Scientific paper

We prove that homogeneous spaces over the q-deformation of simply connected simple compact Lie groups with respect to Poisson-Lie quantum subgroups are equivariantly KK-equivalent to the classical one, extending the nonequivariant case of Neshveyev-Tuset. As applications of this equivariant equivalence we prove the ring isomorphism of the K-group of $G_q$ with respect to the equivariant Kasparov product for the dual discrete quantum group, and the Borsuk-Ulam theorem for quantum spheres.

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