Lie algebras with self-centralizing ad-nilpotent elements
نویسندگان
چکیده
منابع مشابه
Some properties of nilpotent Lie algebras
In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
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The definition of index goes back to Dixmier [3, 11.1.6]. This notion is important in Representation Theory and also in Invariant Theory. By Rosenlicht’s theorem [12], generic orbits of an arbitrary action of a linear algebraic group on an irreducible algebraic variety are separated by rational invariants; in particular, ind g = tr.degK(g). The index of a reductive algebra equals its rank. Comp...
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In this paper we study degenerations of nilpotent Lie algebras. If λ, μ are two points in the variety of nilpotent Lie algebras, then λ is said to degenerate to μ , λ→deg μ , if μ lies in the Zariski closure of the orbit of λ . It is known that all degenerations of nilpotent Lie algebras of dimension n < 7 can be realized via a one-parameter subgroup. We construct degenerations between characte...
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Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90225-4