P. Niroomand

activity

20092024

most citedA note on the Schur multiplier of a nilpotent Lie algebra

53 citations · 284 across the 41 of their papers we have counts for

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20 papers · 1 filter

math.RA2022

The Bogomolov multiplier of Lie superalgebras

Z. Araghi Rostami, P. Niroomand, M. Parviz

In this paper, we extend the notion of the Bogomolov multiplier and the commutativity preserving extension to Lie superalgebras. Moreover, we compute the Bogomolov multiplier of He…

math.RA2022

On the nilpotent Lie superalgebras of small superbreadth

A. Shamsaki, P. Niroomand, M. Ladra

In this paper, we classify finite-dimensional nilpotent Lie superalgebras of superbreadth at most two.

math.RA2022

Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem

A. Shamsaki, P. Niroomand

Let $L$ be a finite dimensional nilpotent Lie algebra and $d$ be the minimal number generators for $L / Z (L) .$ It is known that $dim L / Z (L) = d dim L^{2} - t (L)$ for an integer…

math.RA2021★ 1 cited

On characterizing nilpotent Lie algebra by their multiplier, $ s(L)=6, 7

A. Shamsaki, P. Niroomand

Let $L$ be an $n$ -dimensional non-abelian nilpotent Lie algebra and $s (L) = \frac{1}{2} (n - 1) (n - 2) + 1 - dim M (L)$ where $M (L)$ is the Schur multiplier of a L…

math.RA2020

On the triple tensor product of nilpotent Lie algebras

Afsaneh Shamsaki, Peyman Niroomand

In this paper, we give the explicit structure of $\otimes^{3} H$ and $\land^{3} H$ where $H$ is a generalized Heisenberg Lie algebra of rank at most $2.$ Moreover, for a n…

math.RA2018★ 3 cited

Nilpotent Lie algebras of class $4$ with the derived subalgebra of dimension $3$

Faangis Johari, Peyman Niroomand, Mohsen Parvizi

The paper is devoted to give a full classification of all finite dimensional nilpotent Lie algebras $L$ of class $4$ such that $dim L^{2} = 3.$ Moreover, we classify the capable o…

math.RA2018

Characterizing nilpotent Lie algebras rely on the dimension of their $2$ -nilpotent multipliers

Farangis Johari, Peyman Niroomand

There are some results on nilpotent Lie algebras $L$ investigate the structure of $L$ rely on the study of its $2$ -nilpotent multiplier. It is showed that the dimension of the…

math.RA2018

The capability and certain functors of some nilpotent Lie algebras of class two

Farangis Johari, Peyman Niroomand

Recently, the authors obtained the Schur multiplier, the non-abelian tensor square and the non-abelian exterior square of $d$ -generator generalized Heisenberg Lie algebras of rank…

math.RA2018★ 4 cited

The Bogomolov multiplier of Lie algebras

Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand

In this paper, we extend the notion of the Bogomolov multipliers and the CP-extensions to Lie algebras. Then we compute the Bogomolov multipliers for Abelian, Heisenberg and nilpot…

math.RA2017★ 4 cited

Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two

Farngis Johari, Peyman Niroomand

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 sq…

math.RA2017★ 4 cited

$c$ -nilpotent multiplier and $c$ -capability of the direct sum of Lie algebras

Farangis Johari, Peyman Niroomand, Mohsen Parvizi

In this paper, we determine the behavior of the $c$ -nilpotent multiplier of Lie algebras with respect to the direct sums. Then we give some results on the $c$ -capability of the dir…

math.RA2017★ 14 cited

Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field

Peyman Niroomand, Farangis Johari, Mohsen Parvizi

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algeb…

math.RA2017★ 14 cited

The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras

Farangis Johari, Peyman Niroomand

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 $p$ -gro…

math.RA2017★ 4 cited

Some results on the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand, Farangis Johari

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 boun…

math.RA2015★ 2 cited

Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal

P. Niroomand, F. Johari, M. Parvizi +1

We prove a theorem of splitting for the nonabelian tensor product $L \otimes N$ of a pair $(L, N)$ of Lie algebras $L$ and $N$ in terms of its diagonal ideal $L □ N$ and of th…

math.RA2010★ 13 cited

Some properties on the tensor square of Lie algebras

Peyman Niroomand

In the present paper we extend and improve the results of \cite{bl, br} for the tensor square of Lie algebras. More precisely, for any Lie algebra $L$ with $L / L^{2}$ of finite dimens…

math.RA2010★ 43 cited

Structure of nilpotent Lie algebra by its multiplier

Peyman Niroomand

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 algebr…

math.RA2010★ 50 cited

Capability of Nilpotent Lie algebras with small derived Subalgebra

Peyman Niroomand, Mohsen Parvizi

In this paper, we classify all capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.

math.RA2010★ 8 cited

On the tensor square of non-abelian nilpotent finite dimensional Lie algebras

Peyman Niroomand

For every finite $p$ -group $G$ of order $p^{n}$ with derived subgroup of order $p^{m}$ , Rocco in \cite{roc} proved that the order of tensor square of $G$ is at most $p^{n (n - m)}$ . This…

math.RA2010★ 53 cited

A note on the Schur multiplier of a nilpotent Lie algebra

Peyman Niroomand, Francesco G. Russo

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 $L$ .…

The Bogomolov multiplier of Lie superalgebras

On the nilpotent Lie superalgebras of small superbreadth

Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem

On characterizing nilpotent Lie algebra by their multiplier, $ s(L)=6, 7

On the triple tensor product of nilpotent Lie algebras

Nilpotent Lie algebras of class 4 with the derived subalgebra of dimension 3

Characterizing nilpotent Lie algebras rely on the dimension of their 2-nilpotent multipliers

The capability and certain functors of some nilpotent Lie algebras of class two

The Bogomolov multiplier of Lie algebras

Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two

c-nilpotent multiplier and c-capability of the direct sum of Lie algebras

Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field

The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras

Some results on the Schur multiplier of nilpotent Lie algebras

Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal

Some properties on the tensor square of Lie algebras

Structure of nilpotent Lie algebra by its multiplier

Capability of Nilpotent Lie algebras with small derived Subalgebra

On the tensor square of non-abelian nilpotent finite dimensional Lie algebras

A note on the Schur multiplier of a nilpotent Lie algebra

Nilpotent Lie algebras of class $4$ with the derived subalgebra of dimension $3$

Characterizing nilpotent Lie algebras rely on the dimension of their $2$ -nilpotent multipliers

$c$ -nilpotent multiplier and $c$ -capability of the direct sum of Lie algebras