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arXiv · 2111.11274

Ad-invariant metrics on nonnice nilpotent Lie algebras

Diego Conti·Viviana del Barco·Federico A. Rossi
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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 $2$. In the way of doing so, we introduce a method to construct Lie algebras with ad-invariant metrics called the single extension, as a parallel to the well-known double extension procedure.

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Diego Conti, Viviana del Barco, Federico A. Rossi. 2021-11-22. Ad-invariant metrics on nonnice nilpotent Lie algebras. https://doi.org/10.1142/s0219498825502329

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