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

2024/02/27 by David A. Towers, Towers, David A.
Computer Science · Mathematics · #17A32 #17B05 #17B20 #17B30 #17B50 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2402.17331

openalex publication_date 2024/02/27 · openalex created_date 2024/03/05 · openalex updated_date 2026/07/28

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 sl₂(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.

Related

• On Leibniz algebras whose centralizers are ideals
• Leibniz A-algebras
• Leibniz algebras with an abelian subalgebra of codimension tw0
• Remarks on Leibniz algebras
• On certain classes of algebras in which centralizers are ideals