Abstract
The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted quantum group \({\mathfrak{u}_{r,s}}({F_4})\) as a quotient of Ur,s(F4) is pointed, and of a Drinfel’d double structure under a certain condition. All of Hopf isomorphisms of \({\mathfrak{u}_{r,s}}({F_4})\) are determined, and the necessary and sufficient condition for \({\mathfrak{u}_{r,s}}({F_4})\) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.
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Nai Hong Hu is supported by the NNSF of China (Grant Nos. 12171155, 12071094) and in part by Science and Technology Commission of Shanghai Municipality (Grant No. 22DZ2229014)
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Chen, X.Y., Hu, N.H. & Wang, X.L. Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F4. Acta. Math. Sin.-English Ser. 39, 1053–1084 (2023). https://doi.org/10.1007/s10114-023-1536-9
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DOI: https://doi.org/10.1007/s10114-023-1536-9