Two-Parameter Quantum Groups and Drinfel'd Doubles
Quantum Algebra
2007-05-23 v2 Mathematical Physics
math.MP
Rings and Algebras
Abstract
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n. We show that these quantum groups can be realized as Drinfel'd doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix and a quantum Casimir element. We discuss isomorphisms among these quantum groups and connections with multiparameter quantum groups.
Keywords
Cite
@article{arxiv.math/0011064,
title = {Two-Parameter Quantum Groups and Drinfel'd Doubles},
author = {Georgia Benkart and Sarah Witherspoon},
journal= {arXiv preprint arXiv:math/0011064},
year = {2007}
}
Comments
26 pages, AMS-TeX. Paper rewritten, new material added, some results appear in "Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality"