ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 22, 16 Gromov, Nikolai, Komi Science Center RAS, Syktyvkar, Russia Nonsemisimple Cayley-Klein groups and its quantization. An orthogonal CK groups are the motion groups of N-dimensional spaces of constant curvature. D(ι) is an associative algebra with unit and nilpotent commutative generators. Nonsemisimple CK groups may be realized as the matrix groups over D(ι) [1]. The quantization theory of the simple Lie groups and algebras was developed by FRT [2]. Following slightly modified version of this theory the quantum analogs of the nonsemisimple CK groups are constructed as Hopf algebras of the noncommutative functions over D(ι). The quantum CK algebras are obtained as the dual objects to the corresponding quantum groups. References: 1. N. A. Gromov, Contractions and analytical continuations of the classical groups: unified approach, Komi Science Center, Syktyvkar, 1990 (in Russian). 2. N. Yu. Reshetikhin, L. A. Takhtadjan and L. D. Faddeev, Algebra and Analysis, 1, (1989), 178-206 (in Russian).