Derivations and dimensionally nilpotent derivations in Lie triple algebras

  • Abdoulaye Dembega
  • Amidou Konkobo
  • Moussa Ouattara
Keywords: Dimensionally nilpotent Lie triple algebra, pseudo-idempotent, Jordan algebra, ascending basis, adapted basis

Abstract

In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether it admits an idempotent or a pseudo-idempotent. We study the multiplicative structure of non nil dimensionally nilpotent Lie triple algebras. We show that when n=2p+1 the adapted basis coincides with the canonical basis of the gametic algebra G(2p+2,2) or this one obviously associated to a pseudo-idempotent and if n=2p then the algebra is either one of the precedent case or a conservative Bernstein algebra.

Published
2019-06-25
How to Cite
Dembega, A., Konkobo, A., & Ouattara, M. (2019). Derivations and dimensionally nilpotent derivations in Lie triple algebras. Gulf Journal of Mathematics, 7(2). Retrieved from https://gjom.org/index.php/gjom/article/view/192
Section
Articles