This article is cited in 9 papers

The classical Yang–Baxter equation on alternative algebras: The alternative D-bialgebra structure on Cayley–Dickson matrix algebras

M. E. Goncharov

Novosibirsk State University

Abstract: We consider the Yang–Baxter equations on alternative algebras and prove that the bialgebras induced by the solutions to these equations are alternative D-bialgebras. We describe the alternative D-bialgebra structure on Cayley–Dickson matrix algebras.

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

UDC: 512.554

Received: 27.04.2006

 English version: Siberian Mathematical Journal, 2007, 48:5, 809–823

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