Compact group actions on topological and noncommutative joins

DOI10.1090/PROC/13941zbMATH Open1452.46056arXiv1604.02173OpenAlexW3104801974MaRDI QIDQ4563638

Author name not available (Why is that?)

Publication date: 4 June 2018

Published in: (Search for Journal in Brave)

Abstract: We consider the Type 1 and Type 2 noncommutative Borsuk-Ulam conjectures of Baum, D

k a

browski, and Hajac: there are no equivariant morphisms

A o A c i r c l e d a s t_{d} e l t a H

or

H o A c i r c l e d a s t_{d} e l t a H

, respectively, when

H

is a nontrivial compact quantum group acting freely on a unital

C^{*}

-algebra

A

. Here

A c i r c l e d a s t_{d} e l t a 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 c i r c l e d a s t_{d} e l t a H

. For the classical case

H = m a t h c a l 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.

Full work available at URL: https://arxiv.org/abs/1604.02173

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