TITLE:
Enveloping Lie Algebras of Low Dimensional Leibniz Algebras
AUTHORS:
Massoud Amini, Isamiddin Rakhimov, Seyed Jalal Langari
KEYWORDS:
Leibniz Algebra, Enveloping Lie Algebra, Nilpotent Algebra
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.8,
August
18,
2011
ABSTRACT: We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.