Related papers: About approximate and dual Lie algebras
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…
In this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…
Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.
After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…
We investigate a new class of Lie algebras, which are tame locally extended affine Lie algebras of nullity 1. It is an infinite-rank analog of affine Lie algebras, and their centerless cores are a local version of loop algebras. Such…
The purpose of this paper is to generalize some results on $n$-Lie algebras and $n$-Hom-Lie algebras to $n$-Hom-Lie color algebras. Then we introduce and give some constructions of $n$-Hom-Lie color algebras.
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…
Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
This paper presents a survey of the results and ideas behind the classification of the fine gradings, up to equivalence, on the simple finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It provides an…
For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudo-algebras: every Var-dialgebra can be embedded into an appropriate pseudo-algebra of the…
We invent a new cohomology theory for Lie triple algebras. Using this cohomology, we introduce the notions of 2-term $L_\infty$-triple algebras and Lie triple 2-algebras. We prove that the category of 2-term $L_\infty$-triple algebras is…
Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his classification of Lie subalgebras of the real order-three…
In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey…
In this paper, we introduce the notion of a pre-Lie 2-algebra, which is a categorification of a pre-Lie algebra. We prove that the category of pre-Lie 2-algebras and the category of 2-term pre-Lie$_\infty$-algebras are equivalent. We…
The purpose of this paper is to study the relationships between an $n$-Hom-Lie algebra and its induced $(n+1)$-Hom-Lie algebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived…
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…