Symmetry of quasitriangular structures on some Hopf algebras

Let H be a Hopf algebra. The concept of symmetry of a quasitriangu-lar structure on H is introduced and some properties of a symmetric quasitriangular structure are characterized. We apply this to study quasitriangular structures on small quantum groups and abelian extensions. In particular, the quasitriangular structures on uq(sl2) (if they exist) are proved to be symmetric and all quasi-triangular structures on K(8n, σ, τ), which is a generalization of the well-known 8-dimensional Kac algebra, are determined. 2010 Mathematics Subject Classification. 16T05, 16T25, 17B37.