相关论文: Multipliers of Nilpotent Diassociative Algebras

The paper concerns an analogue of the famous Schur multiplier in the context of associative algebras and a measure of how far its dimension is from being maximal. Applying a methodology from Lie theory, we characterize all…

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur…

The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…

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,…

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…

Let $L$ be an $(m\vert n)$-dimensional nilpotent Lie superalgebra where $m + n \geq 4$ and $n \geq 1$. This paper classifies such nilpotent Lie superalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that $\gamma(L) = m +…

The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative…

Let $ L $ be an $ n $-dimensional nilpotent Lie algebra of nilpotency class $ c $ with the derived subalgebra of dimension $ m $. Recently, Rai proved that the dimension of Schur multiplier of $ L $ is bounded by $…

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong…

It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra $L$ of dimension $n$ is equal to $\frac{1}{2}(n-1)(n-2)+1-s(L)$ for some $ s(L)\geq0 $. The structure of all nilpotent Lie algebras has been given…

By considering the nilpotent Lie algebra with the derived subalgebra of dimension $ 2$, we compute some functors include the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such…

We give a bound on the dimension of the Schur multiplier of a finite dimensional nilpotent Lie algebra which sharpens the earlier known bounds.

In this article, we study the notion of the Schur multiplier $\mathcal{M}(N,L)$ of a pair $(N,L)$ of Lie superalgebras and obtain some upper bounds concerning dimensions. Moreover, we characterize the pairs of finite dimensional (nilpotent)…

A Lie algebra $L$ of dimension $n \ge1 $ may be classified, looking for restrictions of the size on its second integral homology Lie algebra $H_2(L,\mathbb{Z})$, denoted by $M(L)$ and often called Schur multiplier of $L$. In case $L$ is…

The paper is devoted to obtain an upper bound for the Schur multiplier of nilpotent Lie algebras of maximal class. It improves the later upper bounds on the Schur multiplier of such Lie algebras.

Given a pair of nilpotent Lie algebras $A$ and $B$, an extension $0\xrightarrow{} A\xrightarrow{} L\xrightarrow{} B\xrightarrow{} 0$ is not necessarily nilpotent. However, if $L_1$ and $L_2$ are extensions which correspond to lifts of a map…

We introduce an analogue of the famous Schur multiplier in the context of associative trialgebras, or triassociative algebras. The latter were first studied by Loday and Ronco in 2001, and are characterized by three operations and eleven…

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…

The objective of this paper is to develop diassociative analogues of Lie-theoretic results from Peggy Batten's 1993 dissertation. We first prove that covers of diassociative algebras are unique. Second, we show that the multiplier of a…

We provide a bound on the dimension of Schur multiplier of a finite dimensional nilpotent Lie superalgebra which is more precise than the previous bounds on the dimension of Schur multiplier of Lie superalgebra.