Quasitriangular structures on cocommutative Hopf algebras

1997/06/09 by Alexei Davydov, Davydov, A. A.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9706007

openalex publication_date 1997/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 λ-structure on the representation ring of finite group, corresponding to the triangular structure on group ring, is described.

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