Introduction to quantized LIE groups and algebras

Journal Article · Sat Oct 10 00:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92002805· OSTI ID:7135372

Tjin, T ^[1]

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1. Inst. voor Theoretische Fysica, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.

• OSTI ID: 7135372
• Journal Information: International Journal of Modern Physics A; (United States), Vol. 7:25; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
QUANTIZATION
LIE GROUPS
CONFORMAL INVARIANCE
FIELD THEORIES
IRREDUCIBLE REPRESENTATIONS
POISSON EQUATION
QUANTUM MECHANICS
R MATRIX
TENSORS
USES
DIFFERENTIAL EQUATIONS
EQUATIONS
INVARIANCE PRINCIPLES
MATHEMATICS
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
661100* - Classical & Quantum Mechanics- (1992-)