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

Towers, David (2025) Leibniz algebras in which all centralisers of nonzero elements are zero algebras. Communications in Algebra, 53 (2). pp. 681-686. ISSN 0092-7872

Text (Leibniz centraliser transitive algebras)
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Abstract

This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation 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 $sl_2(F)$. A characterisation is then given for solvable Leibniz $CT$-algebras. It is also shown that the class of solvable Leibniz $CT$-algebras is factor closed.