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Leibniz algebras with absolute maximal Lie subalgebras. (English) Zbl 07268065
Summary: A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater than two, we refer to these Leibniz algebras as \(s\)-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz \(s\)-algebras of dimension up to five.
MSC:
17A32 Leibniz algebras
17B55 Homological methods in Lie (super)algebras
18B99 Special categories
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