K-Theory and peiodic cyclic homology of some noncompact quantum algebras

Details K-Theory and peiodic cyclic homology of some noncompact quantum algebras K-Theory and peiodic cyclic homology of some noncompact quantum algebras

2001-09-06

arxiv.org/abs/math/0109042v3

Mathematics

Quantum Algebra

34 pages, no pictures, LaTeX2e

Scientific paper

We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of compact maximal subgroups, without localization. Some noncompact quantum groups and algebras were constructed and their irreducible representations were classified in recent works of Do Ngoc Diep and Nguyen Viet Hai, and Do Duc Hanh by using deformation quantization. In this paper we compute their K-groups, periodic cyclic homology groups and their Chern characters.

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