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

2018/02/16 by Ismael Cohen, Cohen, Ismael, Elmar Wagner +1
Mathematics · #46L65 #46L80 #46L85 #58B32 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1802.06127

openalex publication_date 2018/02/16 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

The paper presents a detailed description of the K-theory and K-homology of\nC*-algebras generated by q-normal operators including generators and the index\npairing. The C*-algebras generated by q-normal operators can be viewed as a\nq-deformation of the quantum complex plane. In this sense, we find deformations\nof the classical Bott projections describing complex line bundles over the\n2-sphere, but there are also simpler generators for the K₀-groups, for\ninstance 1-dimensional Powers-Rieffel type projections and elementary\nprojections belonging to the C*-algebra. The index pairing between these\nprojections and generators of the even K-homology group is computed, and the\nresult is used to express the K₀-classes of the quantized line bundles of any\nwinding number in terms of the other projections.\n

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