Structures Of Generalized Lie Algebras

In this thesis, we study fuzzy subalgebras and fuzzy ideals of n-Lie algebras and we show that the characteristic function of a subalgebra of an n-Lie algebra is a fuzzy subalgebra. Then we introduce some properties of fuzzy subalgebras and fuzzy ideals. Moreover, as a generalization of fuzzy subalgebras, we study(∈,∈ ∨q)-fuzzy subalgebras and we also characterize(∈,∈ ∨q)-fuzzy subalgebras by their level subsets.Next we study the algebra of quotients, triple derivations, triple homomorphisms of a δ-Jordan Lie algebra and construct the maximal algebra of quotients.We also prove that a perfect δ-Jordan Lie algebra in ring R, its derivations are triple derivations, and the triple derivations in its derivation algebras are inner derivations.In the last part, we study some properties of Lie superbialgebras and show that the dual space of a Lie superbialgebra is also a Lie superbialgebra. We also give a su?cient condition to construct a Lie superbialgebra by a Lie superalgebra.