TwoParameter Quantum Groups and Drinfel'd Doubles
Abstract
We investigate twoparameter 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 Rmatrix and a quantum Casimir element. We discuss isomorphisms among these quantum groups and connections with multiparameter quantum groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:math/0011064
 Bibcode:
 2000math.....11064B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Rings and Algebras;
 17B37;
 16W30;
 16W35;
 81R50
 EPrint:
 26 pages, AMSTeX. Paper rewritten, new material added, some results appear in "Representations of TwoParameter Quantum Groups and SchurWeyl Duality"