相关论文: On complete Lie algebras
We introduce a concept, $d$-complete, and show that a Lie algebra is $d$-complete if and only if its full graph is complete.
The authors of this article intend to present some results obtained in the study of biderivations of complete Lie algebras. Firstly they present a matricial approach to do this, which was a useful and explanatory tool not only in the study…
It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any field of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if…
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…
The Lie algebras over the algebra of dual numbers are introduced and investigated.
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…
Complete hom-Lie superalgebra are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
In this paper, we attempt to develop the Schreier theory for two special types extensions of multiplicative Lie algebras.
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In…
The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of…
The aim of this work is to determine the quasi-filiform Lie algebras that are completable. We further prove that for any positive integer $m$ there exists a complete Lie algebra, the second cohomology group of which has dimension greater or…
In this work, the complex Lie affgebra structures on three-dimensional solvable Lie algebras are completely determined.
We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…
A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner…
The notions of conformal Lie 2-algebras and conformal omni-Lie algebras are introduced and studied. It is proved that the category of conformal Lie 2-algebras and the category of 2-term conformal $L_{\infty}$-algebras are equivalent. We…
A complete classification of two-dimensional algebras over algebraically closed fields is provided