ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 22, 19, 43, 58 Do Ngoc Diep, Inst. of Math., NCST of Vietnam On the Structure of Lie Group C*-algebras and Compact Quantum Groups We expose a K-theoretic approach to study group C*-algebras and C*- algebaric compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their compution for C*-algebras of compact Lie groups and C*-algebraic compact quantum groups. References: 1. D. N. Diep, A survey of noncommutative geometry methods for group algebras, J. of Lie Theory, 3(1993),149-176. 2. —, Noncommutative geometry methods for group C*-algebra, 282pp, to appear in Pitman Mathematics Series of Research Notes. 3. D. N. Diep, A. O. Kuku and N. Q. Tho, Noncommutative Chern characters for compact Lie groups C*- algebras, http://www.math.uiuc.edu/K-theory/0257. 4. —, Noncommutative Chern characters for compact quantum groups, preprint 1998.