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arXiv · 1802.06127

K-theory and index pairings for C*-algebras generated by q-normal operators

Ismael Cohen·Elmar Wagner
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Abstract

The paper presents a detailed description of the K-theory and K-homology of C*-algebras generated by q-normal operators including generators and the index pairing. The C*-algebras generated by q-normal operators can be viewed as a q-deformation of the quantum complex plane. In this sense, we find deformations of the classical Bott projections describing complex line bundles over the 2-sphere, but there are also simpler generators for the K_0-groups, for instance 1-dimensional Powers-Rieffel type projections and elementary projections belonging to the C*-algebra. The index pairing between these projections and generators of the even K-homology group is computed, and the result is used to express the K_0-classes of the quantized line bundles of any winding number in terms of the other projections.

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Ismael Cohen, Elmar Wagner. 2018-02-16. K-theory and index pairings for C*-algebras generated by q-normal operators. https://arxiv.org/abs/1802.06127

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