Lie bialgebras with triality and Mal'tsev bialgebras

M. E. Goncharov<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: 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].

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

UDC: 512.554

Received: 10.02.2015

DOI: 10.17377/alglog.2016.55.302

 English version: Algebra and Logic, 2016, 55:3, 198–216

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