Alexei A. Davydov

Department of mathematics and mechanics, Moscow state University,
Moscow, Russia.


"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.

Preprint