Trialgebras and Leibniz 3-algebras
ISSN: 1405-213X, 2296-4495
Year of publication: 2006
Volume: 12
Issue: 2
Pages: 165-178
Type: Article
More publications in: Boletín de la Sociedad Matemática Mexicana: Tercera Serie
Abstract
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.