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.
Scholar Commons Citation
Ben Abdeljelil, Amine, "Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras" (2019). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/7743
