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Note sur les algèbres de Malcev. (A note on Malcev algebras). (French) Zbl 0574.17014
Let A be a Malcev algebra and B a flexible Malcev-admissible one. It is shown that a multiplication can be defined on the vector space \(C=A\oplus B\) so that it becomes a flexible Malcev-admissible algebra containing A as an ideal and B as a subalgebra. This construction is the extension to the Malcev-admissible case of the one given by H. C. Myung [Proc. Am. Math. Soc. 73, 303-307 (1979; Zbl 0397.17001)].
Reviewer: A.Elduque
MSC:
17D10 Mal’tsev rings and algebras
17D25 Lie-admissible algebras
17A20 Flexible algebras
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References:
[1] A. Abd El Malek;Sur les algèbres de Malcev-admissibles, Rend. Acc. Nazionale dei Lincei, Serie VIII, Vol. 68 (1980), 390–396. · Zbl 0467.17002
[2] A. Koulibaly;Algèbres de Malcev en basses dimensions, Thèse de spécialité en Mathématiques, Université de Montpellier II, Montpellier, Juin 1976.
[3] A. I. Malcev;Analytic loops, Mat. Sb. (N. S.), 36 (78) (1955), 569–576 (en russe).
[4] H. C. Myung;Embedding of Lie algebra into Lie-admissible algebra Proc. Amer. Math. Soc. 73 (1979), 303–307. · Zbl 0397.17001 · doi:10.1090/S0002-9939-1979-0518509-8
[5] K. Yamaguti;On the theory of Malcev algebras, Kumamoto J. Sc., Ser. A, 6, no 1 (1963), 9–45. · Zbl 0138.26203
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