Noncommutative Borsuk-Ulam-type conjectures

• Autorzy: Paul F. Baum , Ludwik Dąbrowski , Piotr M. Hajac
• Języki publikacji: EN

Abstrakty

EN

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 $SU_q(2)$.

Kategorie tematyczne

• 46L85: Noncommutative topology
• 58B32: Geometry of quantum groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 106
• Numer: 1
• Strony: 9-18

Daty

wydano

2015

Twórcy

autor

Paul F. Baum

• Mathematics Department, McAllister Building, The Pennsylvania State University, University Park, PA 16802, USA
• Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8 00-656 Warszawa, Poland

autor

Ludwik Dąbrowski

• SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265 34136 Trieste, Italy

autor

Piotr M. Hajac

• Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-656 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc106-0-1