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Leibniz algebras in which all centralizers of nonzero elements are zero algebras

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>1/02/2025
<mark>Journal</mark>Communications in Algebra
Issue number2
Volume53
Number of pages6
Pages (from-to)681-686
Publication StatusPublished
Early online date14/08/24
<mark>Original language</mark>English

Abstract

This paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F)
. A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.