Related papers: Lie properties in associative algebras

The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

We study Lie algebras admitting para-K\"ahler and hyper-para-K\"ahler structures. We give new characterizations of these Lie algebras and we develop many methods to build large classes of examples. Bai considered para-K\"ahler Lie algebras…

Let $L$ be a finite dimensional Lie $F$-algebra endowed with a generalized action by an associative algebra $H$. We investigate the exponential growth rate of the sequence of $H$-graded codimensions $c_n^H(L)$ of $L$ which is a measure for…

The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several…

We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…

A finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler's property if it admits an abelian Lie subalgebra H of dimension at least c(L) - 1. We study the occurrence of this new property in various Lie…

Each flag manifold carries a unique algebra of chiral differential operators. Continuing along the lines of arXiv:0903.1281 we compute the vertex algebra structure on the cohomology of this algebra. The answer is: the tensor product of the…

This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a…

We present a deformation theory approach to the classification of kinematical Lie algebras in 3+1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical Lie algebra and of its…

We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie…

For every field $F$ which has a quadratic extension $E$ we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension $2$. We construct such Lie…

Let k be an infinite field, I an infinite set, V a k-vector-space, and g:k^I\to V a k-linear map. It is shown that if dim_k(V) is not too large (under various hypotheses on card(k) and card(I), if it is finite, respectively countable,…

A solvable Lie algebra L has the property that its nilradical N contains its own centraliser. This is interesting because gives a representation of L as a subalgebra of the derivation algebra of its nilradical with kernel equal to the…

Let L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We provide necessary and also some sufficient conditions in order for its Poisson center and semi-center to be polynomial algebras over…

We introduce the product by generators of complex nilpotent Lie algebras, which is a commutative product obtained from a central extension of the direct sum of Lie algebras. We show that the product preserves also the characteristic…

We discuss how to represent the non-associative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and Super Lie algebra. Then we…

The derived algebra of a symmetrizible Kac-Moody algebra $\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors,…

For a non-abelian Lie algebra $L$ of dimension $n$ with the derived subalgebra of dimension $m$ , the first author earlier proved that the dimension of its Schur multiplier is bounded by $\frac{1}{2}(n+m-2)(n-m-1)+1$. In the current work,…