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2018 K-theory and index pairings for C*-algebras generated by $q$-normal operators
Ismael Cohen, Elmar Wagner
Rocky Mountain J. Math. 48(5): 1485-1510 (2018). DOI: 10.1216/RMJ-2018-48-5-1485

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 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, one 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 quantized line bundles of any winding number in terms of the other projections.

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Ismael Cohen. Elmar Wagner. "K-theory and index pairings for C*-algebras generated by $q$-normal operators." Rocky Mountain J. Math. 48 (5) 1485 - 1510, 2018. https://doi.org/10.1216/RMJ-2018-48-5-1485

Information

Published: 2018
First available in Project Euclid: 19 October 2018

zbMATH: 06958789
MathSciNet: MR3866556
Digital Object Identifier: 10.1216/RMJ-2018-48-5-1485

Subjects:
Primary: 46L65, 46L80, 46L85, 58B32

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 5 • 2018
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