The Quantum Twistor Bundle
Abstract
We investigate the quantum twistor bundle constructed as a -quotient of the quantum instanton bundle of Bonechi, Ciccoli and Tarlini. It is an example of a locally trivial noncommutative bundle fulfilling conditions of the framework recently proposed by Brzezi\'nski and Szyma\'nski. In particular, we give a detailed description of the corresponding -algebra of 'continuous functions' on its noncommutative total space. Furthermore, we analyse a different construction of a quantum instanton bundle due to Landi, Pagani and Reina, find a basis of its polynomial algebra and discover an intriguing and unexpected feature of its enveloping -algebra.
Keywords
Cite
@article{arxiv.2005.03268,
title = {The Quantum Twistor Bundle},
author = {Sophie Emma Zegers and Wojciech Szymański},
journal= {arXiv preprint arXiv:2005.03268},
year = {2022}
}
Comments
The statement in Theorem 4.2. is wrong, the error in the proof lies in the analysis of the joint spectrum. An analysis of irreducible representations of the quantum symplectic sphere where made in the paper "Quantum quaternion spheres" by Bipul Saurabh, where we indeed see that x1 is nonzero