On the subalgebra lattice of a Leibniz algebra

Siciliano, Salvatore and Towers, David (2022) On the subalgebra lattice of a Leibniz algebra. Communications in Algebra, 50 (1). pp. 255-267. ISSN 0092-7872

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Abstract

In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional subalgebras in general results in a number of lattice conditions being weaker than in the Lie case.