Celebratio Mathematica — Baum — Complete Bibliography

Complete Bibliography

Works connected to Nicola Ciccoli

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P. F. Baum, L. Dąbrowski, and P. M. Hajac: “Noncommutative Borsuk–Ulam-type conjectures,” pp. 9–18 in From Poisson brackets to universal quantum symmetries (Warsaw, 18–22 August 2014). Edited by N. Ciccoli and A. Sitarz. Banach Center Publications 106. Instytut Matematyczny PAN (Warsaw), 2015. MR 3469159 Zbl 1343.46064 incollection

Within the framework of free actions of compact quantum groups on unital \( C^* \)-algebras, we propose two conjectures. The first one states that, if \[ \delta:A\to A\otimes_{\min}H \] 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 \( A\circledast_\delta H \). For \( A \) being the \( C^* \)-algebra of continuous functions on a sphere with the antipodal coaction of the \( C^* \)-algebra of functions on \( \mathbb{Z}/2\mathbb{Z} \), 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 \( A\circledast_\delta H \). 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 \( SU_q(2) \).

Ludwik Dąbrowski	Related
Nicola Ciccoli	Related
Andrzej Sitarz	Related
Piotr Mieczysław Hajac	Related