A Locally Trivial Quantum Hopf Fibration
Quantum Algebra
2009-09-25 v3 Operator Algebras
Abstract
The irreducible *-representations of the polynomial algebra O(S^3_{pq}) of the quantum 3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical counterparts. The U(1)-action on O(S^3_{pq}) corresponding for p=1=q to the classical Hopf fibration is proven to be Galois (free). The thus obtained locally trivial Hopf-Galois extension is shown to be relatively projective (admitting a strong connection) and non-cleft. The latter is proven by determining an appropriate Chern-Connes pairing.
Keywords
Cite
@article{arxiv.math/0112317,
title = {A Locally Trivial Quantum Hopf Fibration},
author = {P. M. Hajac and R. Matthes and W. Szymanski},
journal= {arXiv preprint arXiv:math/0112317},
year = {2009}
}
Comments
latex 2e, 23 pages in A4