Trialgebras and Leibniz 3-algebras

  1. Casas, J.M.
Zeitschrift:
Boletín de la Sociedad Matemática Mexicana: Tercera Serie

ISSN: 1405-213X 2296-4495

Datum der Publikation: 2006

Ausgabe: 12

Nummer: 2

Seiten: 165-178

Art: Artikel

Andere Publikationen in: Boletín de la Sociedad Matemática Mexicana: Tercera Serie

Zusammenfassung

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.