Structures of Malcev Bialgebras on a simple non-Lie Malcev algebra

TL;DR

This paper classifies all Malcev bialgebra structures on a specific simple non-Lie Malcev algebra, extending the understanding of algebraic structures related to the classical Yang-Baxter equation.

Contribution

It provides a complete description of Malcev bialgebra structures on a simple non-Lie Malcev algebra, a novel classification in the context of Malcev algebras.

Findings

All Malcev bialgebra structures on the simple non-Lie Malcev algebra are characterized.

The work extends the theory of Lie bialgebras to Malcev algebras.

Connections to solutions of the classical Yang-Baxter equation are discussed.

Abstract

Lie bialgebras were introduced by Drinfeld in studying the solutions to the classical Yang-Baxter equation. The definition of a bialgebra in the sense of Drinfeld (D-bialgebra), related with any variety of algebras, was given by Zhelyabin. In this work, we consider Malcev bialgebras. We describe all structures of a Malcev bialgebra on a simple non-Lie Malcev algebra.