Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if is a free coaction of the C*-algebra H of a non-trivial compact quantum group on a unital C*-algebra A, then there is no H-equivariant *-homomorphism from A to the equivariant join C*-algebra . For A being the C*-algebra of continuous functions on a sphere with the antipodal coaction of the C*-algebra of functions on ℤ/2ℤ, we recover the celebrated Borsuk-Ulam Theorem. The second conjecture states that there is no H-equivariant *-homomorphism from H to the equivariant join C*-algebra . We show how to prove the conjecture in the special case , which is tantamount to showing the non-trivializability of Pflaum’s quantum instanton fibration built from .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-1,
author = {Paul F. Baum and Ludwik D\k abrowski and Piotr M. Hajac},
title = {Noncommutative Borsuk-Ulam-type conjectures},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {9-18},
zbl = {06527818},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-1}
}
Paul F. Baum; Ludwik Dąbrowski; Piotr M. Hajac. Noncommutative Borsuk-Ulam-type conjectures. Banach Center Publications, Tome 104 (2015) pp. 9-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-1/