en
Proceedings chapter
English

q-Deformation of Semisimple and Non-Semisimple Lie Algebras

ContributorsRuegg, Henri
Published inIntegrable Systems, Quantum Groups, and Quantum Field Theories, Editors Ibort, L.A. & Rodríguez, M.A., p. 45-81
Presented at Salamanca, June 15-27, 1992
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. 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
Main files (1)
Proceedings chapter (Published version)
accessLevelRestricted
Identifiers
ISBN9789401048743
325views
0downloads

Technical informations

Creation04/01/2019 3:03:00 PM
First validation04/01/2019 3:03:00 PM
Update time03/15/2023 4:04:27 PM
Status update03/15/2023 4:04:26 PM
Last indexation01/17/2024 5:13:59 AM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack