The local-triviality dimension of actions of compact quantum groups
arXiv:1801.00767
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.
arXiv comment37 pages
References in corpus (11)
- Completely positive maps of order zero
- Noncommutative Geometry Approach to Principal and Associated Bundles
- Equivariant Join and Fusion of Noncommutative Algebras
- Galois-Type Extensions and Equivariant Projectivity
- Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic Groups
- Semiprojectivity with and without a group action
- Rokhlin dimension for compact quantum group actions
- Equivariant semiprojectivity
- The weak Hilbert-Smith conjecture from a Borsuk-Ulam-type conjecture
- Noncommutative Borsuk-Ulam-type conjectures revisited
- Invariants in Noncommutative Dynamics