Related papers: On Engel's Theorem for Leibniz algebras
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…
W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper we show that with the definition of Leibniz-derivation from W. A. Moens the similar result for non Lie Leibniz…
We provide a simple proof of Pascal's Theorem on cyclic hexagons, as well as a generalization by M\"obius, using hyperbolic geometry.
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…
An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.
We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of…
We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.
I prove the group theory analogues of some Lie and Leibniz algebra results on F-hypercentral and F-hypereccentric modules.
Dialgebras are generalizations of associative algebras which give rise to Leibniz algebras instead of Lie algebras. In this paper we study super dialgebras and Leibniz superalgebras, which are $\z_2$-graded dialgebras and Leibniz algebras.…
In a recent study of Engel Lie rings, Serena Cicalo` and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of…
An analog of Picard's little theorem for entire functions of matrices is proved.
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
This paper deals with the classification of Leibniz central extensions of a naturally graded filiform Lie algebra. We choose a basis with respect to that the table of multiplication has a simple form. In low dimensional cases isomorphism…
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the…
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it coincides with its idealizer IL(S). In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.
In the present note a generalization of Borel-Cantelli Lemma is proposed.