Principal fibrations over noncommutative spheres
Quantum Algebra
2018-11-14 v1 Mathematical Physics
math.MP
Abstract
We present examples of noncommutative four-spheres that are base spaces of -principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of . We give conditions for the components of the Connes--Chern character of the projection to vanish but the second (the top) one. The latter is then a non zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.
Cite
@article{arxiv.1804.07032,
title = {Principal fibrations over noncommutative spheres},
author = {Michel Dubois-Violette and Xiao Han and Giovanni Landi},
journal= {arXiv preprint arXiv:1804.07032},
year = {2018}
}