25 Years of Quantum Groups: from Definition to Classification

A. Stolin

Abstract


In mathematics and theoretical physics, quantum groups are certain non-commutative, non-cocommutative Hopf algebras, which first appeared in the theory of quantum integrable models and later they were formalized by Drinfeld and Jimbo. In this paper we present a classification scheme for quantum groups, whose classical limit is a polynomial Lie algebra. As a consequence we obtain deformed XXX and XXZ Hamiltonians. 

Keywords


Lie bialgebra; quantum group; Yang-Baxter equation; quantization; classical twist; quantum twist; integrable model

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague