This article is cited in 5 papers

Jordan D-Bialgebras and Symplectic Forms on Jordan Algebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: It is shown that a symplectic structure determined on a Jordan algebra induces a symplectic structure on the adjoint Lie KKT-algebra. It is proven that Jordan bialgebras of some type defined on semisimple finite-dimensional Jordan algebras are triangular Jordan bialgebras.

Key words: Jordan bialgebra, Lie bialgebra, triangular bialgebra, Yang–Baxter equation, Kantor–Köcher–Tits construction.

UDC: 512.554

Received: 22.03.1999

 English version: Siberian Advances in Mathematics, 2000, 10:2, 142–150

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