Exotic Quantum Double,Its Universal R-matrix And Their Representations

Details Exotic Quantum Double,Its Universal R-matrix And Their Representations Exotic Quantum Double,Its Universal R-matrix And Their Representations

1992-12-10

arxiv.org/abs/hep-th/9212066v1

J.Math.Phys. 34 (1993) 3440-3452

Physics

High Energy Physics

High Energy Physics - Theory

19 pages,ITP.SB-9271

Scientific paper

10.1063/1.530035

The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld's quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum doubles that are the q-deformations for Lie algebras or Lie superalgebras. By studying its representation theory,many-parameter representations of the exotic quantum double are obtained with an explicit example associated with Lie algebra $A_2$ .The multi-parameter R-matrices for the quantum Yang-Baxter equation can result from the universal R-matrix of this exotic quantum double and these representattions.

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