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Article

Paal, Eugen
Note on analytic Moufang loops. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 45 (2004), issue 2, pp. 349-354
MSC: 17D10, 20N05, 22A30 | MR 2075282 | Zbl 1099.22004
Keywords:
Moufang loop; Mal'tsev algebra; generalized Maurer-Cartan equations; triality
Summary:
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.
References:
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[3] Mal'tsev A.I.: Analytic loops. Matem. Sb. 36 (1955), 569-576 (in Russian). MR 0069190
[4] Paal E.: An Introduction to Moufang Symmetry. Preprint F-42 Institute of Physics, Tartu (1987 (in Russian)). MR 1241991
[5] Loos O.: Über eine Beziehung zwischen Malcev-Algebren und Lie-Tripelsystemen. Pacific J. Math. 18 (1966), 553-562. MR 0199236 | Zbl 0145.04202
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[7] Yamaguti Y.: On the theory of Malcev algebras. Kumamoto J. Sci. A6 (1963), 9-45. MR 0167507 | Zbl 0138.26203
[8] Schafer R.D.: An Introduction to Nonassociative Algebras. Academic Press New York (1966). MR 0210757 | Zbl 0145.25601
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