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Leibniz triple systems. (English) Zbl 1301.17005
The authors define Leibniz triple systems in a functorial manner using the KP algorithm which converts identities for algebras into identities for dialgebras. They verify that Leibniz triple systems are natural analogues of Lie triple systems by showing that both the iterated bracket in a Leibniz algebra and the permuted associator in a Jordan dialgebra satisfy the defining identities for Leibniz triple systems. The authors construct the universal Leibniz envelopes of Leibniz triple systems and prove that every identity satisfied by the iterated bracket in a Leibniz algebra is a consequence of the defining identities for Leibniz triple systems.

MSC:
17A40 Ternary compositions
17A32 Leibniz algebras
17B35 Universal enveloping (super)algebras
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