Trialgebras and Leibniz 3-algebras

• Autores: José Manuel Casas Mirás
• Localización: Boletín de la Sociedad Matemática Mexicana: Tercera Serie, ISSN 1405-213X, ISSN-e 2296-4495, Vol. 12, Nº. 2, 2006, págs. 165-178
• Idioma: inglés
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• Resumen

  • We analyze the relationship between trialgebras (K-vector spaces equipped with three binary associative operations) and Leibniz 3-algebras (K-vector spaces equipped with a ternary bracket that verifies an identity which is a generalization of the Leibniz identity for Leibniz algebras) in a similar way as dialgebras are related to Leibniz algebras. The universal enveloping algebra U3L(ℒ) of a Leibniz 3-algebras L is constructed and the equivalence between the categories of right U3L(ℒ)-modules and ℒ-representations is proved.