"Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebr" by Amine Ben Abdeljelil

Graduation Year

2019

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Mohamed Elhamdadi, Ph.D.

Co-Major Professor

Abdenacer Makhlouf, Ph.D.

Committee Member

Brian Curtin, Ph.D.

Committee Member

Dmytro Savchuk, Ph.D.

Committee Member

Mahmood H. Nachabe, Ph.D.

Keywords

Ternary Algebra, n-ary Algebras, BiHom Algebras, Derivations, Quasi-Derivations

Abstract

We generalize the results of Leger and Luks and other researchers about generalized derivations to the cases of ternary Lie algebras and n-BiHom Lie algebras. We investigate the derivations algebras of ternary Lie algebras induced from Lie algebras, we explore the subalgebra of quasi-derivations and give their properties. Moreover, we give a classification of the derivations algebras for low dimensional ternary Lie algebras.

For the class of n-BiHom Lie algebras, we study the algebras of generalized derivations and prove that the algebra of quasi-derivations can be embedded in the derivation algebra of a larger n-BiHom Lie algebra.

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