in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space H(g, k) for certain Lie algebras g. Among these Lie algebras are filiform CNLAs of dimension n ≤ 14. It turns out that there are many examples of CNLAs which admit a symplectic structure. A generalization of a sympletic structure is an affine structure on a Lie algebra.

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application, we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which can serve as counterexamples for various Burnside type questions.

This paper studies the relationship between representations of a Lie group and representations of its Lie algebra. We will make the correspondence in two steps: First we shall prove that a given representation of a Lie group will provide us with a corresponding representation of its Lie algebra. Second, we shall go backwards and see whether a given representation of a Lie algebra will have a co...

The concept of (α, β)-fuzzy Lie algebras over an (α, β)-fuzzy field is introduced. We provide characterizations of an (∈,∈ ∨q)-fuzzy Lie algebra over an (∈,∈ ∨q)-fuzzy field. 2000 MSC: 17B99, 08A72

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