Degenerations of nilpotent Lie algebras
نویسنده
چکیده
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 characteristically nilpotent filiform Lie algebras. As an application it follows that for any dimension n ≥ 7 there exist examples of degenerations of nilpotent Lie algebras which cannot be realized via a one–parameter subgroup.
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