Quasitriangular structures on cocommutative Hopf algebras

Details Quasitriangular structures on cocommutative Hopf algebras Quasitriangular structures on cocommutative Hopf algebras

1997-06-09

arxiv.org/abs/q-alg/9706007v1

Mathematics

Quantum Algebra

Latex, 22 pages

Scientific paper

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.

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