Two-Parameter Quantum Groups and Drinfel'd Doubles

Details Two-Parameter Quantum Groups and Drinfel'd Doubles Two-Parameter Quantum Groups and Drinfel'd Doubles

2000-11-09

arxiv.org/abs/math/0011064v2

Mathematics

Quantum Algebra

26 pages, AMS-TeX. Paper rewritten, new material added, some results appear in "Representations of Two-Parameter Quantum Group

Scientific paper

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.

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