Let H be the C*algebra of a nontrivial compact quantum group acting freely on a unital C*algebra A. Baum, Dabrowski and Hajac conjectured that there does not exist an equivariant *homomorphism from A to the equivariant noncommutative join C*algebra A*H. When A is the C*algebra of functions on a sphere, and H is the C*algebra of functions on Z/2Z acting antipodally on the sphere, then the conjecture becomes the celebrated BorsukUlam theorem. Recently, Passer proved the conjecture when H is the commutative C*algebra of functions on a nontrivial compact group with a torsion element. The first goal of this talk is to show how to extend this result to the quantum setting. Next, with a stronger assumption that our compact quantum group is a qdeformation of a compact connected semisimple Lie group, we prove a stronger result that there exists a finitedimensional representation of the compact quantum group such that, for any C*algebra A admitting a character, the finitely generated projective module associated with A*H via this representation is not stably free. (Based on joint work with L. Dabrowski and S. Neshveyev.)
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Noncommutative BorsukUlamtype conjectures revisited
Research Group:
Piotr M. Hajac
Institution:
IMPAN
Location:
A136
Schedule:
Friday, February 3, 2017  16:00
Abstract:
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