We extend the basic fact that every ideal of a finite dimensional semisimple Lie algebra has a unique complement to the case of closed ideals of prosemisimple Lie algebras. We prove that if A is a closed ideal of a prosemisimple Lie algebra L = lim ←−−Ln (n ∈ N), where the Ln are finite dimensional semisimple Lie algebras, then there exists a unique ideal B of L such that L = A ⊕ B. Mathematics...

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

The notion of a non-associative universal enveloping algebra for a Lie triple system arises when Lie triple systems are considered as Bol algebras (more generally, Sabinin algebras). In this paper a new construction for these universal enveloping algebras is given, and their properties are studied. It is shown that universal enveloping algebras of Lie triple systems have surprisingly few ideals...

In this paper, the intuitionistic fuzzy Lie sub-superalgebras and ideals of Lie superalgebras are studied further. We define the intuitionistic fuzzy quotient Lie superalgebra by an intuitionistic fuzzy Lie ideal and prove that it is a Lie superalgebra. The intuitionistic fuzzy set of quotient Lie superalgebra is also considered. Finally, solvable intuitionistic fuzzy Lie ideals and nilpotent i...

In this paper, we have introduced the notion of vague Lie ideal and have studied their related properties. The cartesian products of vague Lie ideals are discussed. In particular, the Lie homomorphisms between the vague Lie ideals of a Lie algebra and the relationship between the domains and the co-domains of the vague Lie ideals under these Lie homomorphisms are investigated. Mathematics subje...