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

Towers, David A. (2024) Leibniz algebras in which all centralizers of nonzero elements are zero algebras. Communications in Algebra. ISSN 0092-7872

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.