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

Abstract

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.

19 pages,ITP.SB-9271

Cited by in corpus (2)

• Quantization of Drinfel'd doubles
• The Drinfeld double gl(n) \oplus t_n