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arXiv · 1609.06824

Convex PBW-type Lyndon Bases and Restricted Two-Parameter Quantum Group of Type $F_4$

Xiaoyu Chen·Naihong Hu·Xiuling Wang
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Abstract

We determine convex PBW-type Lyndon bases for two-parameter quantum groups $U_{r,s}(F_4)$ with detailed commutation relations. We construct a finite-dimensional Hopf algebra $\mathfrak u_{r,s}(F_4)$, as a quotient of $U_{r,s}(F_4)$ by a Hopf ideal generated by certain central elements, which 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 which are important for seeking the possible new pointed objects in low order with $(\ell, 210)\ne 1$. Finally, necessary and sufficient conditions for $\mathfrak u_{r,s}(F_4)$ to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

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Xiaoyu Chen, Naihong Hu, Xiuling Wang. 2016-09-22. Convex PBW-type Lyndon Bases and Restricted Two-Parameter Quantum Group of Type $F_4$. https://arxiv.org/abs/1609.06824

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