Geodesic
Embedding Mal'tsev coalgebras into Lie coalgebras with triality
Algebra i logika, Tome 52 (2013) no. 1, pp. 34-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that any Mal'tsev coalgebra embeds in a Lie coalgebra with triality. Thus Mikheev's known result for Mal'tsev algebras is fully extended to Mal'tsev coalgebras.
Keywords: Mal'tsev algebra, Lie algebra, weakly inner derivation
Mots-clés : Mal'tsev coalgebra, Lie coalgebra, pseudoderivation. 
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M. E. Goncharov; V. N. Zhelyabin. Embedding Mal'tsev coalgebras into Lie coalgebras with triality. Algebra i logika, Tome 52 (2013) no. 1, pp. 34-56. http://geodesic.mathdoc.fr/item/AL_2013_52_1_a2/

[1] G. Glauberman, “On loops of odd order. II”, J. Algebra, 8 (1968), 393–414 | DOI | MR | Zbl

[2] S. Doro, “Simple Moufang loops”, Math. Proc. Camb. Philos. Soc., 83 (1978), 377–392 | DOI | MR | Zbl

[3] P. O. Mikheev, “O gruppakh, obertyvayuschikh lupy Mufang”, UMN, 48:2(290) (1993), 191–192 | MR | Zbl

[4] M. W. Liebeck, “The classification of finite simple Moufang loops”, Math. Proc. Camb. Philos. Soc., 102 (1987), 33–47 | DOI | MR | Zbl

[5] A. N. Grishkov, A. V. Zavarnitsine, “Lagrange's theorem for Moufang loops”, Math. Proc. Camb. Philos. Soc., 139:1 (2005), 41–57 | DOI | MR | Zbl

[6] A. I. Maltsev, “Analiticheskie lupy”, Matem. sb., 36(78):3 (1955), 569–576 | MR | Zbl

[7] E. N. Kuzmin, I. P. Shestakov, “Neassotsiativnye struktury”, Algebra–6, Itogi nauki i tekhniki. Sovr. probl. matem. Fundam. napravl., 57, VINITI, M., 1990, 179–266 | MR | Zbl

[8] P. O. Mikheev, “O vlozhenii algebr Maltseva v algebry Li”, Algebra i logika, 31:2 (1992), 167–173 | MR | Zbl

[9] A. Grishkov, “Lie algebras with triality”, J. Algebra, 266:2 (2003), 698–722 | DOI | MR | Zbl

[10] W. Michaelis, “Lie coalgebras”, Adv. Math., 38:1 (1980), 1–54 | DOI | MR | Zbl

[11] J. A. Anquela, T. Cortés, F. Montaner, “Nonassociative coalgebras”, Commun. Algebra, 22:12 (1994), 4693–4716 | DOI | MR | Zbl

[12] V. N. Zhelyabin, “Konstruktsiya Kantora–Kekhera–Titsa dlya iordanovykh koalgebr”, Algebra i logika, 35:2 (1996), 173–189 | MR | Zbl

[13] V. N. Zhelyabin, “Iordanovy (super)koalgebry i (super)koalgebry Li”, Sib. matem. zh., 44:1 (2003), 87–111 | MR | Zbl

[14] V. N. Zhelyabin, “Embedding of Jordan copairs into Lie coalgebras”, Commun. Algebra, 35:2 (2007), 561–576 | DOI | MR | Zbl

[15] B. O'Neill, Semi-Riemannian geometry, With applications to relativity, Pure Appl. Math., 103, Academic Press, New York–London etc., 1983 | MR

[16] I. Bajo, S. Benayadi, “Lie algebras admitting a unique quadratic structure”, Commun. Algebra, 25:9 (1997), 2795–2805 | DOI | MR | Zbl

[17] I. Bajo, S. Benayadi, A. Medina, “Sympletic structures on quadratic Lie algebras”, J. Algebra, 316:1 (2007), 174–188 | DOI | MR | Zbl