Two-Parameter Quantum Groups and Drinfel’d Doubles
by Benkart, Georgia; Witherspoon, Sarah
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras
$${\mathfrak{g}}{\mathfrak{l}}_n $$
and
$${\mathfrak{s}}{\mathfrak{l}}_n $$
. 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.
DOI: 10.1023/B:ALGE.0000031151.86090.2e
Print publication date: 8/1/2004
View article on SpringerLink
