Finite-dimensional Jordan algebras admitting the structure of a Jordan bialgebra

We define the concepts of a triangular and a quasitriangular Jordan bialgebras. It is proved that a finite-dimensional Jordan algebra J over an algebraically closed field Φ admits the structure of a quasitriangular Jordan bialgebra with nonzero comultiplication, provided that J is not a direct sum of fields, algebras H(Φ₂) and H(Φ₃), null extensions of Φ, and of algebras with zero multiplication. Supported by RFFR grant No. 98-01-01142. Translated fromAlgebra i Logika, Vol. 38, No. 1, pp. 40–67, January–February, 1999.