Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B

Details Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B

2008-12-17

arxiv.org/abs/0812.3343v6

J. Geom. Phys., 60 (2010), 430-453

Mathematics

Quantum Algebra

reduced version: 32+(3) pages

Scientific paper

10.1016/j.geomphys.2009.11.005

We construct convex PBW-type Lyndon bases for two-parameter quantum groups U_{r,s}({so}_{2n+1}) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group u_{r,s}({so}_{2n+1}) (r, s are roots of unity) is of Drinfeld double. All of Hopf isomorphisms of u_{r,s}({so}_{2n+1}), as well as u_{r,s}({sl}_n) are determined. Finally, necessary and sufficient conditions for u_{r,s}({so}_{2n+1}) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

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