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Equivariant Comparison of Quantum Homogeneous Spaces

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Abstract

We consider the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups and their Poisson–Lie quantum subgroups. We prove the deformation invariance in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev and Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-homology of G q with respect to the coproduct of C(G q ), and an analogue of the Borsuk–Ulam theorem for quantum spheres.

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Author notes

  1. Makoto Yamashita

    Present address: Department of Mathematics, Ochanomizu University, Ohtsuka 2-1-1, Bunkyo-ku, 112-8610, Tokyo, Japan

Authors and Affiliations

  1. Dipartimento di Matematica, Università Degli Studi di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Rome, Italy

    Makoto Yamashita

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  1. Makoto Yamashita
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Correspondence to Makoto Yamashita.

Additional information

Communicated by Y. Kawahigashi

Supported in part by the ERC Advanced Grant 227458 OACFT “Operator Alge bras and Conformal Field Theory”.

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Yamashita, M. Equivariant Comparison of Quantum Homogeneous Spaces. Commun. Math. Phys. 317, 593–614 (2013). https://doi.org/10.1007/s00220-012-1594-9

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