Free actions on C*-algebra suspensions and joins by finite cyclic groups

DOI10.1512/IUMJ.2018.67.6238zbMATH Open1411.46050arXiv1510.04100OpenAlexW2296116784MaRDI QIDQ4962363

Author name not available (Why is that?)

Publication date: 2 November 2018

Published in: (Search for Journal in Brave)

Abstract: We present a proof for certain cases of the noncommutative Borsuk-Ulam conjectures proposed by Baum, Dk{a}browski, and Hajac. When a unital

C^{*}

-algebra

A

admits a free action of

m a t h b b Z / k m a t h b b Z

,

k g e q 2

, there is no equivariant map from

A

to the

C^{*}

-algebraic join of

A

and the compact "quantum" group

C (m a t h b b Z / k m a t h b b Z)

. This also resolves Dk{a}browski's conjecture on unreduced suspensions of

C^{*}

-algebras. Finally, we formulate a different type of noncommutative join than the previous authors, which leads to additional open problems for finite cyclic group actions.

Full work available at URL: https://arxiv.org/abs/1510.04100

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