Quasitriangular structures on cocommutative Hopf algebras

Abstract

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular, quasitriangular structure on group algebra is defined by the pairs of normal inclusions of an finite abelian group and by invariant bimultiplicative form on it. The structure is triangular in the case of coinciding inclusions and skewsymmetric form. The nonstandart $\lambda$-structure on the representation ring of finite group, corresponding to the triangular structure on group ring, is described.