A note on outer derivations of Leibniz algebras

Authors

G. R. Biyogmam, Georgia College & State University
C. Tcheka, University of Dschang

Document Type

Article

Publication Date

2020

Publication Title

Communications in Algebra

Abstract

In this article, we discuss completeness of non-Lie Leibniz algebras by studying various conditions under which they admit outer derivations. Our study focusses particularly on the class of non-perfect Leibniz algebras whose center is not contained in the Leibniz kernel. We extend to this class of Leibniz algebras several well-known results on derivations of Lie algebras. In particular, we show that solvable Leibniz algebras in this class are not complete. Also, we show that non-stem Leibniz algebras admit outer central derivations. Finally, we independently show that semisimple non-Lie Leibniz algebras are complete.

Department

Mathematics

Comments

© 2021 Taylor & Francis Group, LLC.

DOI

10.1080/00927872.2020.1867154

Recommended Citation

Biyogmam, G. R., & Tcheka, C. (2020). A note on outer derivations of Leibniz algebras. Communications in Algebra.