Related papers: A Generalization of A Leibniz Geometrical Theorem
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…
Leibniz algebras are certain generalization of Lie algebras. In this paper we survey the important results in Leibniz algebras which are analogs of corresponding results in Lie algebras. In particular we highlight the differences between…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi…
In this paper, we propose a generalization of a congruence due to Carlitz.
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.
This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.
We introduce the notion of a generalized metric n-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric n-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras…
The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove…
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.
We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are…