Convex PBWtype Lyndon Bases and Restricted TwoParameter Quantum Group of Type $F_4$
Abstract
We determine convex PBWtype Lyndon bases for twoparameter quantum groups $U_{r,s}(F_4)$ with detailed commutation relations. We construct a finitedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.06824
 arXiv:
 arXiv:1609.06824
 Bibcode:
 2016arXiv160906824C
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 31 pages. arXiv admin note: text overlap with arXiv:0812.3343