The book is devoted to the study of algebras of functions on quantum groups. The authors' approach to the subject is based on the parallels with symplectic geometry, allowing the reader to use geometric intuition in the theory of quantum groups. The book includes the theory of Poisson Lie groups (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions, and the theory of quantum Weyl groups. This book can serve as a text for an introduction to the theory of quantum groups.
Introduction Poisson Lie groups Quantized universal enveloping algebras Quantized algebras of functions Quantum Weyl group and the universal quantum $R$-matrix Bibliography.
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- ID: 9780821803363
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