Compact group actions on topological and noncommutative joins
Open Access
- 17 April 2018
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 146 (8), 3217-3232
- https://doi.org/10.1090/proc/13941
Abstract
We consider the Type 1 and Type 2 noncommutative Borsuk-Ulam conjectures of Baum, Dabrowski, and Hajac: there are no equivariant morphisms A -> A circle star(delta) H or H -> A circle star(delta) H, respectively, when H is a nontrivial compact quantum group acting freely on a unital C*-algebra A. Here A circle star(delta) H denotes the equivariant noncommutative join of A and H; this join procedure is a modification of the topological join that allows a free action of H on A to produce a free action of H on A circle star(delta) H. For the classical case H = C(G), G a compact group, we present a reduction of the Type 1 conjecture and counterexamples to the Type 2 conjecture. We also present some examples and conditions under which the Type 2 conjecture does hold.Keywords
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Funding Information
- National Science Foundation (1565226, 1300280, 1363250, Zuckerman Fellowship, 346300, 2015-2019 Matching Fund)
This publication has 2 references indexed in Scilit:
- Free actions on C*-algebra suspensions and joins by finite cyclic groupsIndiana University Mathematics Journal, 2018
- Equivariant Join and Fusion of Noncommutative AlgebrasSymmetry, Integrability and Geometry: Methods and Applications, 2015