## Quantum groups.(Spanish. English summary)Zbl 1113.17304

Khakimdjanov, Yusupdjan (ed.) et al., Algebra and operator theory. Proceedings of the colloquium, Tashkent, Uzbekistan, September 29–October 5, 1997. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-5094-4/hbk). 213-236 (1998).
From the text: The author gives a concise introduction to the theory of quantum groups from the point of view of braided tensor categories. He first introduces tensor categories and gives some examples: vector spaces, modules over a bialgebra and the quantum enveloping algebra of $$\text{sl}(2)$$. Then definitions and results about braided categories, the Yang-Baxter equation, braided bialgebras, braided groups, the quantum double, etc. are given. The exposition is very clear. Some applications are also supplied.
For the entire collection see [Zbl 0908.00015].

### MSC:

 17B37 Quantum groups (quantized enveloping algebras) and related deformations 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory