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Algebra i logika, 2016, Volume 55, Number 3, Pages 300–327
DOI: https://doi.org/10.17377/alglog.2016.55.302 (Mi al743) 		 
Lie bialgebras with triality and Mal'tsev bialgebras

M. E. Goncharovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.17377/alglog.2016.55.302
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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00014
Supported by RFBR, project No. 14-01-00014.
Received: 10.02.2015
English version:
Algebra and Logic, 2016, Volume 55, Issue 3, Pages 198–216
DOI: https://doi.org/10.1007/s10469-016-9389-2
Bibliographic databases:
Document Type: Article
UDC: 512.554
Language: Russian
Citation: M. E. Goncharov, “Lie bialgebras with triality and Mal'tsev bialgebras”, Algebra Logika, 55:3 (2016), 300–327; Algebra and Logic, 55:3 (2016), 198–216
Citation in format AMSBIB
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\paper Lie bialgebras with triality and Mal'tsev bialgebras
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\vol 55
\issue 3
\pages 300--327
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\jour Algebra and Logic
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\issue 3
\pages 198--216
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