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

2016/09/22 by Xiaoyu Chen, Naihong Hu, Chen, Xiaoyu +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1609.06824

openalex publication_date 2016/09/22 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We determine convex PBW-type Lyndon bases for two-parameter quantum groups U_r,s(F₄) with detailed commutation relations. We construct a finite-dimensional Hopf algebra \mathfrak u_r,s(F₄), as a quotient of U_r,s(F₄) 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(F₄) are determined which are important for seeking the possible new pointed objects in low order with (ℓ, 210)≠ 1. Finally, necessary and sufficient conditions for \mathfrak u_r,s(F₄) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

Cited by

• Simple Modules and PI Structure of the Two-Parameter Quantized Algebra U⁺_r,s(B₂)

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