25 Years of Quantum Groups: from Definition to Classification

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

quantum twist

quantization

quantum group

integrable model

Lie bialgebra

Yang-Baxter equation

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

Publication and Content Type

art (subject category)

vet (subject category)