Proceedings chapter
English

q-Deformation of Semisimple and Non-Semisimple Lie Algebras

ContributorsRuegg, Henri
Presented atSalamanca, June 15-27, 1992
Published inIbort, L.A. & Rodríguez, M.A. (Ed.), Integrable Systems, Quantum Groups, and Quantum Field Theories, p. 45-81
PublisherDordrecht : Kluwer Academic Publishers
Collection
  • NATO ASI Series : advanced science institutes series. Series C, Mathematical and physical sciences; 409
Publication date1993
Abstract

We give an elementary introduction to the Drinfeld-Jimbo procedure of the quantum deformation Uq(g) of semisimple Lie algebras g. The q—Serre relations are discussed in some detail, in the Chevalley and the Cartan—Weyl basis. We review the real forms of g and Uq(g). The general procedure is illustrated by the examples Uq(sℓ(2)) and Uq (so(5, ℂ)). After some general considerations on non-semisimple Lie algebras, we discuss in detail the quantum deformation of the Poincaré algebra, involving the contraction of Uq(so(3, 2)). Some physical consequences are mentioned.

Citation (ISO format)
RUEGG, Henri. q-Deformation of Semisimple and Non-Semisimple Lie Algebras. In: Integrable Systems, Quantum Groups, and Quantum Field Theories. Ibort, L.A. & Rodríguez, M.A. (Ed.). Salamanca. Dordrecht : Kluwer Academic Publishers, 1993. p. 45–81. (NATO ASI Series : advanced science institutes series. Series C, Mathematical and physical sciences) doi: 10.1007/978-94-011-1980-1_3
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