Quantum line bundles on noncommutative sphere
摘要
Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a multiplicative structure in their family. Also, we compute a pairing between certain quantum line bundles and finite dimensional representations of the NC sphere in the spirit of the NC index theorem. A new approach to constructing the differential calculus on a NC sphere is suggested. The approach makes use of the projective modules in question and gives rise to a NC de Rham complex being a deformation of the classical one.
引用
@article{arxiv.math/0110013,
title = {Quantum line bundles on noncommutative sphere},
author = {D. Gurevich and P. Saponov},
journal= {arXiv preprint arXiv:math/0110013},
year = {2009}
}
备注
LaTeX file, 15 pp, no figures. Some clarifying remarks are added at the beginning of section 2 and into section 5