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Noncommutative Borsuk-Ulam-type conjectures

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Baum P., Dąbrowski L., Hajac P.

Banach Center Publications

2015

tom 106

nr 1

9-18

Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if $δ: A → A ⨂_{min} H$ 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 $A ⊛_δ H$. 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 $A ⊛_δ H$. We show how to prove the conjecture in the special case $A = C(SU_q(2)) = H$, which is tantamount to showing the non-trivializability of Pflaum's quantum instanton fibration built from $SU_q(2)$.

Ograniczanie wyników

1 Banach Center Publications

1 Baum P.

1 Dąbrowski L.

1 Hajac P.

1 2015

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Noncommutative Borsuk-Ulam-type conjectures