Graduation Year


Document Type




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.


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


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.