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.
arXiv Mathematics e-prints
- Pub Date:
- November 2000
- Mathematics - Quantum Algebra;
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- Mathematics - Rings and Algebras;
- 26 pages, AMS-TeX. Paper rewritten, new material added, some results appear in "Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality"