Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F4

作者：Chen, Xiao Yu; Hu, Nai Hong; Wang, Xiu Ling^*

来源：ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2023, 39(6): 1053-1084.

DOI：10.1007/s10114-023-1536-9

• Convex PBW-type Lyndon basis
• restricted 2-parameter quantum groups
• integrals
• ribbon Hopf algebra

The convex PBW-type Lyndon basis for two-parameter quantum group U-r,U-s(F-4) is given. Assume that rs(-1) is a primitive l-th root of unity with l odd, then the restricted quantum group u(r,s)(F-4) as a quotient of U-r,U-s(F-4) is pointed, and of a Drinfel'd double structure under a certain condition. All of Hopf isomorphisms of u(r,s)(F-4) are determined, and the necessary and sufficient condition for u(r,s)(F-4) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.

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  南开大学