This article is cited in 1 paper

Lie bialgebras arising from alternative and Jordan bialgebras

M. E. Goncharov

Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk

Abstract: We consider connection between simple alternative D-bialgebras and Lie bialgebras. We prove that each finite-dimensional alternative noncommutative algebra over an algebraically closed field may be equipped with the nontrivial structure of an alternative D-bialgebra.

Keywords: alternative bialgebra, Jordan bialgebra, classical Yang–Baxter equation, nonassociative coalgebra, Cayley–Dickson algebra.

UDC: 512.554

Received: 26.11.2008

 English version: Siberian Mathematical Journal, 2010, 51:2, 215–228

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