Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Hu, Naihong¹  Wang, Xiuling^2,3 

[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Convex PBW-type Lyndon basis;    Restricted two-parameter quantum groups;    Integrals;    Ribbon Hopf algebra;   

DOI  :  10.1016/j.geomphys.2009.11.005

来源: Elsevier

【 摘 要 】

We construct convex PBW-type Lyndon bases for two-parameter quantum groups Ur,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 a Drinfel'd double. All 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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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