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Quantum line bundles on noncommutative sphere

D. Gurevich·P. Saponov
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Abstract

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.

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BibTeXRIS

D. Gurevich, P. Saponov. 2002-06-27. Quantum line bundles on noncommutative sphere. https://doi.org/10.1088/0305-4470%2F35%2F45%2F310

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