in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley–Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M1,M2 ∈ L =⇒ M1M2 − M2M1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that L1 = ML...

Multisymplectic geometry is a generalization of symplectic geometry suitable for n-dimensional field theories, in which the nondegenerate 2-form of symplectic geometry is replaced by a nondegenerate (n + 1)-form. The case n = 2 is relevant to string theory: we call this ‘2-plectic geometry.’ Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, the ...

In this paper, first we introduce the notion of a Reynolds operator on an n-Lie algebra and illustrate relationship between operators derivations algebra. We give cohomology theory study infinitesimal deformations using second group. Then NS-n-Lie algebras, which are generalizations both algebras n-pre-Lie algebras. show that gives rise to together with representation itself. Nijenhuis naturall...

suppose $g$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$f,$ $p=mn$ is a maximal parabolic subgroup of $g,$ $frak{n}$ is‎ ‎the lie algebra of the unipotent radical $n.$ under the adjoint‎ ‎action of its stabilizer in $m,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.

assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

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.

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...