"Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras" by Guy Roger Biyogmam, José Manuel Casas et al.
 

Document Type

Article

Publication Date

2020

Publication Title

Publicationes Mathematicae

Abstract

In this paper, we introduce the notion of a Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, and call them Lie-central derivations. We provide a characterization of Lie-stem Leibniz algebras by their Lie-central derivations, and prove several properties of the Lie algebra of Lie-central derivations for Lie-nilpotent Leibniz algebras of class 2. We also introduce ID∗-Lie-derivations. An ID∗-Lie-derivation of a Leibniz algebra g is a Lie-derivation of g in which the image is contained in the second term of the lower Lie-central series of g, and which vanishes on Lie-central elements. We provide an upper bound for the dimension of the Lie algebra IDLie∗ (g) of ID∗-Lie-derivation of g, and prove that the sets IDLie∗ (g) and IDLie∗ (q) are isomorphic for any two Lie-isoclinic Leibniz algebras g and q.

Department

Mathematics

Volume Number

97

Issue Number

1

First Page

217

Last Page

239

Comments

© 2020 University of Debrecen, Institute of Mathematics. All rights reserved.

DOI

10.5486/PMD.2020.8810

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