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Ad-invariant metrics on nonnice nilpotent Lie algebras
Preprint
22 November 2021
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Abstract
We proved in previous work that all real nilpotent Lie algebras of dimension up to \(10\) carrying an ad-invariant metric are nice. In this paper we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than \(10\) and every nilpotency step greater than \(2\).