Papers by Afsaneh Shamsaki
Communications in Algebra, Jun 22, 2020
Abstract In this note, we give two bounds for the order of Schur multiplier of groups of order pn... more Abstract In this note, we give two bounds for the order of Schur multiplier of groups of order pn and class c with derived subgroup of order They improve the earlier upper bounds on the order of Schur multiplier of such groups, in particular the bounds of Moravec and Rai when
Rendiconti Del Circolo Matematico Di Palermo, Feb 6, 2019
Let L be a non-abelian nilpotent Lie algebra of dimension n and $$s(L)=\frac{1}{2}(n-1)(n-2)+1- \... more Let L be a non-abelian nilpotent Lie algebra of dimension n and $$s(L)=\frac{1}{2}(n-1)(n-2)+1- \dim {\mathcal {M}}(L)$$s(L)=12(n-1)(n-2)+1-dimM(L), where $${\mathcal {M}}(L)$$M(L) denotes the Schur multiplier of L. For a non-abelian nilpotent Lie algebra, we know $$ s(L)\ge 0 $$s(L)≥0 and the structure of all nilpotent Lie algebras are well known for $$ s(L) \in \lbrace 0,1,2,3 \rbrace $$s(L)∈{0,1,2,3} in several papers. The current paper is devoted to obtain the structure of all nilpotent Lie algebras L, when $$ s(L)=4 $$s(L)=4.
Mathematical Reports, 2023
It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra L o... more It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra L of dimension n is equal to 1 2 (n − 1)(n − 2) + 1 − s(L) for some s(L) ≥ 0. The structure of all nilpotent Lie algebras has been given for s(L) ≤ 4 in several papers. Here, we are going to give the structure of all non-abelian nilpotent Lie algebras for s(L) = 5.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
arXiv (Cornell University), Sep 6, 2022
In this paper, we classify finite-dimensional nilpotent Lie superalgebras of superbreadth at most... more In this paper, we classify finite-dimensional nilpotent Lie superalgebras of superbreadth at most two.
Publicationes Mathematicae Debrecen
arXiv (Cornell University), Aug 22, 2022
In this paper, we show that converse of the Schur's theorem is true for Lie superalgebra with the... more In this paper, we show that converse of the Schur's theorem is true for Lie superalgebra with the minimal generator number pairs (|) of / () when sdim 2 is finite superdimentional. Also, we define () = λ(2 , ,) − sdim / (), where λ(2 , ,) = (.dim 2 0 + .dim 2 1 , .dim 2 0 + .dim 2 1) and we classify the structure of all finite superdimentional nilpotent Lie superalgebras when () ∈ {(0, 0), (1, 0), (0, 1), (2, 0), (0, 2), (1, 1)}.
arXiv (Cornell University), Aug 22, 2022
Let L be a finite dimensional nilpotent Lie algebra and d be the minimal number generators for L/... more 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 t(L) ≥ 0. In this paper, we classify all finite dimensional nilpotent Lie algebras L when t(L) ∈ {0, 1, 2}. We find also a construction, which shows that there exist Lie algebras of arbitrary t(L).
Communications in Algebra, 1998
The nilpotent Lie algebras L of dimension n whose multipliers have dimension ½n(n-1)-t(L) have be... more The nilpotent Lie algebras L of dimension n whose multipliers have dimension ½n(n-1)-t(L) have been found in [2] for t(L) = 0,1,2. Using a different method, we find similar results for t(L) = 3,4,5,6. The first author is extending the results to t(L) = 7 and 8.
Results in Mathematics, Feb 23, 2022
Let L ∼ = I 1 ⋊ A(1) such that I 1 ∼ = 37A = x 1 ,. .. , x 6 , x 8 | [x 1 , x 2 ] = x 5 , [x 2 , ... more Let L ∼ = I 1 ⋊ A(1) such that I 1 ∼ = 37A = x 1 ,. .. , x 6 , x 8 | [x 1 , x 2 ] = x 5 , [x 2 , x 3 ] = x 6 , [x 2 , x 4 ] = x 8 and A(1) = x 7. Then the relations of L are as follow.
Communications in Algebra
Bulletin of the Iranian Mathematical Society
Given a nilpotent Lie algebra L of dimension ≤ 6 on an arbitrary field of characteristic = 2, we ... more Given a nilpotent Lie algebra L of dimension ≤ 6 on an arbitrary field of characteristic = 2, we show a direct method which allows us to detect the capability of L via computations on the size of its nonabelian exterior square L ∧ L. For dimensions higher than 6, we show a result of general nature, based on the evidences of the low dimensional case, focusing on generalized Heisenberg algebras. Indeed we detect the capability of L ∧ L via the size of the Schur multiplier M (L/Z ∧ (L)) of L/Z ∧ (L), where Z ∧ (L) denotes the exterior center of L. 1. Statement of the results and terminology Throughout this paper all Lie algebras are considered over a prescribed field F and [ , ] denotes the Lie bracket. Let L and K be two Lie algebras. Following [6, 7], an action of L on K is an F-bilinear map L × K → K given by (l, k) → l k satisfying [l,l ′ ] k = l (l ′ k) − l ′ (l k) and l [k, k ′ ] = [ l k, k ′ ] + [k, l k ′ ], for all l, l ′ ∈ L and k, k ′ ∈ K. These actions are compatible, if k l k ′ = k ′ l k and l k l ′ = l ′ k l for all l, l ′ ∈ L and k, k ′ ∈ K. Now L ⊗ K is the Lie algebra generated by the symbols l ⊗ k subject to the relations c(l ⊗ k) = cl ⊗ k = l ⊗ ck, (l + l ′) ⊗ k = l ⊗ k + l ′ ⊗ k,
Results in Mathematics, 2022
Let L ∼ = I 1 ⋊ A(1) such that I 1 ∼ = 37A = x 1 ,. .. , x 6 , x 8 | [x 1 , x 2 ] = x 5 , [x 2 , ... more Let L ∼ = I 1 ⋊ A(1) such that I 1 ∼ = 37A = x 1 ,. .. , x 6 , x 8 | [x 1 , x 2 ] = x 5 , [x 2 , x 3 ] = x 6 , [x 2 , x 4 ] = x 8 and A(1) = x 7. Then the relations of L are as follow.
arXiv: Commutative Algebra, 2019
It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra $L$... more 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 for $ s(L) \leq 4 $ in several papers. Here, we are going to give the structure of all non-abelian nilpotent Lie algebras for $s(L)=5$.
In this paper, we give the explicit structure of $ \otimes^{3} H $ and $ \wedge^{3} H $ where $ H... more In this paper, we give the explicit structure of $ \otimes^{3} H $ and $ \wedge^{3} H $ where $ H $ is a generalized Heisenberg Lie algebra of rank at most $ 2. $ Moreover, for a non-abelian nilpotent Lie algebra $ L, $ we obtain an upper bound for the dimension of $ \otimes^{3} L.
In this paper, the structure of all finite-dimensional nilpotent Lie algebras of class two with d... more In this paper, the structure of all finite-dimensional nilpotent Lie algebras of class two with derived subalgebra of dimension two over an arbitrary field $ \mathbb{F} $ is determined. Furthermore, we give the structure of the Schur multiplier of such Lie algebras.
Quaestiones Mathematicae, 2020
We give a new bound for the dimension of the Schur multiplier of an ndimensional nilpotent Lie al... more We give a new bound for the dimension of the Schur multiplier of an ndimensional nilpotent Lie algebra of class c with the derived subalgebra of dimension n − 2. This new bound sharpens the earlier upper bounds on the dimension of Schur multiplier of such Lie algebras, especially for Lie algebras of maximal class.
Communications in Algebra, 2020
In this note, we give two bounds for the order of Schur multiplier of groups of order p n and cla... more In this note, we give two bounds for the order of Schur multiplier of groups of order p n and class c with derived subgroup of order p nÀ2 ðp 6 ¼ 2Þ: They improve the earlier upper bounds on the order of Schur multiplier of such groups, in particular the bounds of Moravec and Rai when jG 0 j ¼ p nÀ2 : ARTICLE HISTORY
Quaestiones Mathematicae, 2019
Let L be an n-dimensional nilpotent Lie algebra of nilpotency class c with the derived subalgebra... more 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 1 2 (n − m − 1)(n + m) − min{n−m,c} i=2 n − m − i. In this paper, we obtain the structure of all nilpotent Lie algebras that attain this bound.
International Journal of Algebra and Computation, 2019
Let [Formula: see text] be a non-abelian nilpotent Lie algebra of dimension [Formula: see text] a... more Let [Formula: see text] be a non-abelian nilpotent Lie algebra of dimension [Formula: see text] and [Formula: see text] be its Schur multiplier. It was proved by the second author the dimension of the Schur multiplier is equal to [Formula: see text] for some [Formula: see text]. In this paper, we classify all nilpotent Lie algebras of maximal class for [Formula: see text]. The dimension of Schur multiplier of such Lie algebras is also bounded by [Formula: see text]. Here, we give the structure of all nilpotent Lie algebras of maximal class [Formula: see text] when [Formula: see text] and then we show that all of them are capable.
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Papers by Afsaneh Shamsaki