The R-matrix of quantum doubles of Nichols algebras of diagonal type

2013/04/21 by Ivan Angiono, Angiono, Ivan, Hiroyuki Yamane +1
Mathematics · #16T05 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16T05

paper · pdf · doi:10.48550/arxiv.1304.5752

22 pages

arxiv created 2014/05/26 · arxiv updated 2014/05/27

Abstract

Let H be the quantum double of a Nichols algebra of diagonal type. We compute the R-matrix of 3-uples of modules for general finite-dimensional highest weight modules over H. We calculate also a multiplicative formula for the universal R-matrix when H is finite dimensional.

Related

• The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type
• Simple Modules of the Quantum Double of the Nichols Algebra of Unidentified Diagonal Type \mathfrakufo(7)
• R-matrices for quantum affine algebras and Khovanov-Lauda-Rouquier algebras, I
• Lifting of Nichols Algebras of Type B₂, with an Appendix: A generalization of the q-binomial theorem
• The R-matrix of the quantum toroidal algebra