Lie bialgebras with triality and Mal'tsev bialgebras

M. E. Goncharov

Algebra i logika, Tome 55 (2016) no. 3, pp. 300-327.

Résumé

We consider the relationship between Mal’tsev bialgebras and Lie bialgebras with triality, and also between symplectic Mal’tsev algebras and symplectic Lie algebras with triality. The given relations generalize a connection between Mal’tsev algebras and Lie algebras with triality, revealed by P. O. Mikheev [Algebra i Logika, 31, No. 2 (1992), 167–173], and a connection between Mal'tsev coalgebras and Lie coalgebras with triality, explored by M. E. Goncharov and V. N. Zhelyabin [Algebra i Logika, 52, No. 1 (2013), 34–56].

Détail

Keywords: Mal'tsev algebra, Mal'tsev bialgebra, Lie algebra, Lie bialgebra, classical Yang–Baxter equation, symplectic form.

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