Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups

Details Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups

2005-05-27

arxiv.org/abs/math/0505614v1

J. Algebra 301 (2006), no. 1, 378-405

Mathematics

Representation Theory

25 pages AMSTeX

Scientific paper

We find the defining structures of two-parameter quantum groups $U_{r,s}(\frak g)$ corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between $(U_{r,s}(\frak g), < ,>)$ and its associated object $(U_{s^{-1}, r^{-1}}(\frak g), < | >)$.

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