Noncommutative Balls and Mirror Quantum Spheres
Operator Algebras
2014-02-26 v2 Quantum Algebra
Abstract
Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the `even-dimensional' case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C*-algebras and polynomial algebras of the objects in question are defined and analyzed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes and Szymanski for `dimension 2', and leads to a new class of quantum spheres (already on the C*-algebra level) in all `even-dimensions'.
Cite
@article{arxiv.math/0701799,
title = {Noncommutative Balls and Mirror Quantum Spheres},
author = {Jeong Hee Hong and Wojciech Szymanski},
journal= {arXiv preprint arXiv:math/0701799},
year = {2014}
}
Comments
20 pages