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- Title
Two-Parameter Quantum Groups and Drinfel'd Doubles.
- Authors
Georgia Benkart; Sarah Witherspoon
- Abstract
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras <img src="/fulltext-image.asp?format=htmlnonpaginated&src=UQ2154266J823031_html\10468_2004_Article_5270185_TeX2GIFIE1.gif" border="0" alt=" $${\mathfrak{g}}{\mathfrak{l}}_n $$ " /> and <img src="/fulltext-image.asp?format=htmlnonpaginated&src=UQ2154266J823031_html\10468_2004_Article_5270185_TeX2GIFIE2.gif" border="0" alt=" $${\mathfrak{s}}{\mathfrak{l}}_n $$ " />. 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.
- Publication
Algebras & Representation Theory, 2004, Vol 7, Issue 3, p261
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1023/b:alge.0000031151.86090.2e