Ad-invariant metrics on nonnice nilpotent Lie algebras

Autor(es)

Conti, D. ; del Barco, V. ; Rossi, F. A.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 26-pg., 2024-04-05.

Resumo

We proved in previous work that all real nilpotent Lie algebras of dimension up to 10 carrying an ad-invariant metric are nice, i.e. they admit a nice basis in the sense of Lauret et al. 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. (AU)

• Processo FAPESP: 21/09197-8 - Métricas invariantes especiais em grupos de Lie e seus quocientes compactos
• Beneficiário: Viviana Jorgelina Del Barco
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 23/15089-9 - Aspectos da geometria conforme e Riemanniana em grupos de Lie e seus quocientes compactos.
• Beneficiário: Viviana Jorgelina Del Barco
• Modalidade de apoio: Auxílio à Pesquisa - Regular