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On the subalgebra lattice of a Leibniz algebra

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<mark>Journal publication date</mark>31/01/2022
<mark>Journal</mark>Communications in Algebra
Issue number1
Volume50
Number of pages13
Pages (from-to)255-267
Publication StatusPublished
Early online date2/08/21
<mark>Original language</mark>English

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.