Infinitesimal R-matrices for some families of Hopf algebras

2024/12/03 by Bottegoni, Lucrezia, Renda, Fabio, Sciandra, Andrea
#FOS: Mathematics #Primary 16T05 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 16E40

paper · doi:10.48550/arxiv.2412.02350

Abstract

Given a bialgebra H such that the associated trivial topological bialgebra H[[ℏ]] admits a quasitriangular structure R=R(1⊗ 1+ℏχ+O(ℏ²)), one gets a distinguished element χ∈ H ⊗ H which is an infinitesimal R-matrix, according to the definition given in [1]. In this paper we classify infinitesimal R-matrices for some families of well-known Hopf algebras, among which are the generalized Kac-Paljutkin Hopf algebras H_2n², the Radford Hopf algebras H_(r,n,q), and the Hopf algebras E(n).

Related

• On the quasitriangular structures of abelian extensions of Z₂
• Quasitriangular structures on cocommutative Hopf algebras
• R-matrices and Hopf algebra quotients
• Hopf algebras under finiteness conditions
• On infinite-dimensional Hopf algebras