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Characterizing Nilpotent n-Lie Algebras by Their Multiplier
Results in Mathematics ( IF 1.1 ) Pub Date : 2021-01-09 , DOI: 10.1007/s00025-020-01326-w
Hamid Darabi , Mehdi Eshrati , Homayoon Arabyani

For every nilpotent n -Lie algebra A of dimension d , t ( A ) is defined by $$t(A)=\left( {\begin{array}{c}d\\ n\end{array}}\right) -\dim {\mathcal {M}}(A)$$ t ( A ) = d n - dim M ( A ) , where $${\mathcal {M}}(A)$$ M ( A ) denotes the Schur multiplier of A . In this paper, we classify all nilpotent n -Lie alegbras A satisfying $$t(A)=9,10$$ t ( A ) = 9 , 10 . We also classify all nilpotent n -Lie algebras for $$11\le t(A)\le 16$$ 11 ≤ t ( A ) ≤ 16 when $$n\ge 3$$ n ≥ 3 .

中文翻译:

用乘数表征幂零 n-李代数

对于维度 d 的每个幂零 n -李代数 A , t ( A ) 定义为 $$t(A)=\left( {\begin{array}{c}d\\ n\end{array}}\right ) -\dim {\mathcal {M}}(A)$$ t ( A ) = dn - dim M ( A ) ,其中 $${\mathcal {M}}(A)$$ M ( A ) 表示A 的舒尔乘数。在本文中,我们对满足 $$t(A)=9,10$$t ( A ) = 9 , 10 的所有幂零 n -Lie alegbras A 进行分类。当 $$n\ge 3$$ n ≥ 3 时,我们还将所有幂零 n -Lie 代数分类为 $$11\le t(A)\le 16$$ 11 ≤ t ( A ) ≤ 16 。
更新日期:2021-01-09
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