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A. Shamsaki

Publications and source records attributed to A. Shamsaki.

6 recordsLinked to original sources
arXiv2024

On converse of the Schur's theorem for nilpotent Lie superalgebras

In this paper, we establish a converse to Schur's theorem for Lie superalgebras \( L \), focusing on cases where the minimal generator number pairs \((p \vert q)\) of \( L/Z(L) \) are considered, and where the superdimension \( \mathrm{sdim} L^{2} \) is finite. We introduce a new invariant \( st(L) \), which plays a key role in the classification of finite-dimensional nilpotent Lie superalgebras. Specifically, we classify the structure of all such Lie superalgebras \( L \) when \( st(L) \in \{(0,0), (1,0), (0,1), (2,0), (0,2), (1,1)\} \).

math.AC↗
arXiv2022

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

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)\geq 0. $ In this paper, we classify all finite dimensional nilpotent Lie algebras $ L $ when $ t(L)\in \lbrace 0, 1, 2 \rbrace.$ We find also a construction, which shows that there exist Lie algebras of arbitrary $ t(L). $

math.RA↗
arXiv2021

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

Let $ L $ be an $ n $-dimensional non-abelian nilpotent Lie algebra and $ s(L)=\frac{1}{2}(n-1)(n-2)+1-\dim \mathcal{M}(L) $ where $ \mathcal{M}(L) $ is the Schur multiplier of a Lie algebra $ L. $ The structures of nilpotent Lie algebras $ L $ when $ s(L)\in \lbrace 0,1,2,3,4,5\rbrace $ are determined. In this paper, we classify all non-abelian nilpotent Lie algebras $ L $ when $ s(L)=6,7. $

math.RA↗
arXiv2018

Nilpotent Lie algebras having the Schur multiplier of maximum dimension

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 $ \frac{1}{2}(n-m-1)(n+m)-\sum\limits_{i=2}^ {min\lbrace n-m,c\rbrace} n-m-i $. In this paper, we obtain the structure of all nilpotent Lie algebras that attain this bound.

math.AC↗