Related papers: Lie Dimension Subrings

A commutative Poisson subalgebra of the Poisson algebra of polynomials on the Lie algebra of n x n matrices over ${\Bbb C}$ is introduced which is the Poisson analogue of the Gelfand-Zeitlin subalgebra of the universal enveloping algebra.…

For a finite dimensional Lie algebra $L$, it is known that $s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L)$ is non negative. Moreover, the structure of all finite nilpotent Lie algebras is characterized when $s(L)=0,1$ in \cite{ni,ni4}. In…

We prove that there exists just one pair of complex four-dimensional Lie algebras such that a well-defined contraction among them is not equivalent to a generalized IW-contraction (or to a one-parametric subgroup degeneration in…

Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of four dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear…

We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of…

The aim of this article is to discuss the $n$-derivation algebras of Lie color algebras. It is proved that, if the base ring contains $\frac{1}{n-1}$, $L$ is a perfect Lie color algebra with zero center, then every triple derivation of $L$…

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…

Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L)$, where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of…

Let $n>1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$, are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, which are generated by an element of degree $1$ and an element…

We study the minimal dimension of maximal commutative subalgebras of the matrix algebra $M_n(k)$ over an algebraically closed field. While examples with dimension strictly smaller than n are known for $n \geq 14$, no such examples are known…

The numerical dimension is a numerical measure of the positivity of a pseudo-effective divisor $L$. There are several proposed definitions of the numerical dimension due to Nakayama (2004) and Boucksom et al. (2004). We prove the equality…

We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension less than 7 over a finite field.

Given a connected semisimple Lie group $G$ and an arithmetic subgroup $\Gamma$, it is well-known that each irreducible representation $\pi$ of $G$ occurs in the discrete spectrum $L^2_{\text{disc}}(\Gamma\backslash G)$ of…

In this lecutre note, we consider infinite dimensional Lie algebras of generalized Jacobi matrices $\mathfrak{g}J(k)$ and $\mathfrak{gl}_\infty(k)$, which are important in soliton theory, and their orthogonal and symplectic subalgebras. In…

We categorize all non-abelian nilpotent Lie superalgebras of dimension $(m|n)$, where $1\leq s(L)\leq 10$, and $s(L)$ is a non-negative integer defined by Nayak. Furthermore, we classify the structure of all Lie superalgebras of dimension…

The aim of this paper is to investigate in which sense, for $n\geq 3$, $n$-Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [10] and [5]) but after analysing those we come to the…

I show that an (n+2)-dimensional n-Lie algebra over an algebraically closed field must have a subalgeba of codimension 1.

We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In…

Let $\varepsilon>0$. We construct an explicit, full-measure set of $\alpha \in[0,1]$ such that if $\gamma \in \mathbb{R}$ then, for almost all $\beta \in[0,1]$, if $\delta \in \mathbb{R}$ then there are infinitely many integers $n\geq 1$…