相关论文: The Schur multiplier of an $n$-Lie superalgebra

Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and…

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…

Given a finite dimensional Lie algebra $L$ let $I$ be the augmentation ideal in the universal enveloping algebra $U(L)$. We study the conditions on $L$ under which the $Ext$-groups $Ext (k,k)$ for the trivial $L$-module $k$ are the same…

Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra…

We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie…

Let A_k denote the twisted group algebra of the symmetric group S_k, whose representations correspond to the nonlinear projective representations of S_k. We establish a duality relation between A_k and a Lie superalgebra q(n), sometimes…

We describe an algorithm to compute the Schur multipliers of all nilpotent Lie $p$-rings in the family defined by a symbolic nilpotent Lie $p$-ring. Symbolic nilpotent Lie $p$-rings can be used to describe the isomorphism types of…

Let $G$ be the semidirect product $N \rtimes \mathbb{R}$, where $N$ is a stratified Lie group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$,…

Let $V$ be a complex vector space with a non-degenerate symmetric bilinear form and $\mathbb S$ an irreducible module over the Clifford algebra $Cl(V)$ determined by this form. A supertranslation algebra is a $\mathbb Z$-graded Lie…

We consider the representation dimension, for fixed $n\geq2$, of ordinary and quantised Schur algebras $S(n,r)$ over a field $k$. For $k$ of positive characteristic $p$ we give a lower bound valid for all $p$. We also give an upper bound in…

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…

In this article, we characterize plurisubharmonic functions of Lelong number one at the origin, such that the germ of the associated multiplier ideal sheaf is nontrivial: in arbitrary complex dimension, their singularity must be the sum of…

In this paper, we study the maximal dimension $\alpha(L)$ of abelian subalgebras and the maximal dimension $\beta(L)$ of abelian ideals of m-dimensional 3-Lie algebras $L$ over an algebraically closed field. We show that these dimensions do…

Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the…

In 1998, G. Ellis defined the Schur multiplier of a pair $(G,N)$ of groups and mentioned that this notion is a useful tool for studying pairs of groups. In this paper, we characterize the structure of a pair of finite $p$-groups $(G,N)$ in…

In this paper, we use the theory of simplicial groups to develop the Schur multiplier of a pair of groups $(G,N)$ to the Baer invariant of it, $\mathcal{V}M(G,N)$, with respect to an arbitrary variety $\mathcal{V}$. Moreover, we present…

A chain $S_0 < S_1 < \ldots < S_n = L$ is a {\em maximal chain} if each $S_i$ is a maximal subalgebra of $S_{i+1}$. The subalgebra $S_0$ in such a series is called an {\em $n$-maximal} subalgebra. There are many interesting results…

Levi's theorem decomposes any arbitrary Lie algebra over a field of characteristic zero, as a direct sum of a semisimple Lie algebra (named Levi factor) and its solvable radical. Given a solvable Lie algebra $R$, a semisimple Lie algebra…

We complete the solution of the problem of finding the universal central extension of the matrix superalgebras $\mathfrak{sl}(m, n, A)$ where $A$ is an associative superalgebra and computing $H_2\big(\mathfrak{sl}(m, n, A)\big)$. The…

Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…