On Leibniz algebras whose centralizers are ideals

This paper concerns the study of Leibniz algebras, a natural generalization of Lie algebras, from the perspective of centralizers of elements. We study conditions on Leibniz algebras under which centralizers of all elements are ideals. We call a Leibniz algebra, a CL-algebra if centralizers of all e...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Das, Pratulananda, Saha, Ripan
Format: Article
Language:English
Subjects:
Algebra
Lie groups
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Summary:This paper concerns the study of Leibniz algebras, a natural generalization of Lie algebras, from the perspective of centralizers of elements. We study conditions on Leibniz algebras under which centralizers of all elements are ideals. We call a Leibniz algebra, a CL-algebra if centralizers of all elements are ideals. We discuss nilpotency of CL-algebras.
ISSN:2331-8422