Harmonic analysis in one-parameter metabelian nilmanifolds.

Ghorbel, Amira

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The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on $ℝ^{n}$ with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

Some necessary and sufficient conditions for nilpotent $n$ -Lie superalgebras

Baoling Guan, Liangyun Chen, Yao Ma (2014)

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The paper studies nilpotent $n$ -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for $n$ -Lie superalgebras which is a generalization of those for $n$ -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent $n$ -Lie superalgebras and obtain several sufficient conditions for an $n$ -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal...

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