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THE NONCOMMUTATIVE CHERN–CONNES CHARACTER OF THE LOCALLY COMPACT QUANTUM NORMALIZER OF SU(1,1) IN

DO NGOC DIEP

Institute of Mathematics, National Center for Science and Technology of Vietnam, 18 Hoang Quoc Viet Road, Cau Giay District, 10307 Hanoi, Vietnam

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https://doi.org/10.1142/S0129167X0400234XCited by:1 (Source: Crossref)

Abstract

We observe that the von Neumann envelop of (i.e. the smallest von Neumann algebra that contains) the quantum algebra of functions on the normalizer of the group SU(1,1)≅SL(2,ℝ) in via deformation quantization contains the von Neumann algebraic quantum normalizer of SU(1,1) in the frame work of Waronowicz–Korogodsky, see ([8, Introduction and Sec. 1, Definition 1]), i.e. the C*-envelop or von Neumann envelop (W*-envelop) of the algebraic Hopf algebra. We then use the technique of reduction to the maximal subgroup to compute the K-theory, the periodic cyclic homology and the corresponding Chern–Connes character.

Keywords:

AMSC: 19K35, 19L10, 46L85, 81R60

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