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Lie triple supersystems associated with Maltsev superalgebras. (Supersystèmes triples de Lie associés aux superalgèbres de Malcev.) (French) Zbl 1106.17309
The authors continue their study on Mal’tsev superalgebras on a field \(K\) of characteristic zero [see Afr. Mat., Sér. III 14, 5–17 (2002; Zbl 1106.17308); A. Ouedraogo, ibid. 14, 45–51 (2002; Zbl 1034.49046)]. The properties of Mal’tsev super-representations and weak super representation are given. The notion of representation of Lie triple super systems is defined and it is proved that a super-representation of a Mal’tsev superalgebra \(M\) is a super-representation of the Lie triple super systems associated with \(M\).
MSC:
17D10 Mal’tsev rings and algebras
17A40 Ternary compositions
17A70 Superalgebras
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