Research Article

The role of derivations in the nilpotence and semisimplicity of Lie triple systems

Published in: Quaestiones Mathematicae
Volume 47 , issue 7 , 2024 , pages: 1437–1459

DOI: 10.2989/16073606.2024.2320439

Author(s): Hani Abdelwahab Mansoura University, Egypt , Antonio J. Calderón Martín University of Cádiz, Spain , Moustafa Mahanna Mansoura University, Egypt

Keywords: 17A30 , 17A40 , 17B30 , 17D99 , 14D06 , 14L30 , PLEASE SUPPLY?

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Abstract

We explore the role derivations of a Lie triple system play in the nilpotence and semisimplicity of T. In particular analogous to two theorems of Jacobson for Lie algebras, (by giving a sufficient condition for the nilpotence of T in terms of the existence of an invertible derivation, and in terms of the existence of certain automorphisms), are stated. The connections between the Lie algebra of derivations of and the semisimplicity of T are also studied.

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