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arXiv · 1801.00767

The local-triviality dimension of actions of compact quantum groups

Eusebio Gardella·Piotr M. Hajac·Mariusz Tobolski·Jianchao Wu
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Abstract

We define the local-triviality dimension for actions of compact quantum groups on unital C*-algebras. The resulting compact quantum principal bundle is said to be locally trivial when this dimension is finite. For commutative C*-algebras, this notion recovers the standard definition of local triviality of compact principal bundles. We prove that actions with finite local-triviality dimension are automatically free. Then we apply this new notion to prove the noncommutative Borsuk-Ulam-type conjecture under the assumption that a compact quantum group admits a non-trivial classical subgroup whose induced action has finite local-triviality dimension. This is a noncommutative extension of the Borsuk-Ulam-type theorem for locally trivial principal bundles.

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Eusebio Gardella, Piotr M. Hajac, Mariusz Tobolski, Jianchao Wu. 2018-01-02. The local-triviality dimension of actions of compact quantum groups. https://arxiv.org/abs/1801.00767

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