On nonsingular two-step nilpotent Lie algebras

A 2-step nilpotent Lie algebra n is called non-singular if ad X : n → [n, n] is onto for any X /∈ [n, n]. We explore non-singular algebras in several directions, including the classification problem (isomorphism invariants), the existence of canonical inner products (nilsolitons) and their automorph...

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Detalles Bibliográficos
Autores principales: Lauret, Jorge Rubén, Oscari, Francisco David
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
Nonsingular
2-step
Nilpotent
Pfaffian
Acceso en línea:http://hdl.handle.net/11086/30059
https://doi.org/10.48550/arXiv.1209.3060
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-30059
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Nonsingular
2-step
Nilpotent
Pfaffian
spellingShingle Nonsingular
2-step
Nilpotent
Pfaffian
Lauret, Jorge Rubén
Oscari, Francisco David
On nonsingular two-step nilpotent Lie algebras
topic_facet Nonsingular
2-step
Nilpotent
Pfaffian
description A 2-step nilpotent Lie algebra n is called non-singular if ad X : n → [n, n] is onto for any X /∈ [n, n]. We explore non-singular algebras in several directions, including the classification problem (isomorphism invariants), the existence of canonical inner products (nilsolitons) and their automorphism groups (maximality properties). Our main tools are the moment map for certain real reductive representations and the Pfaffian form of a 2-step algebra, which is a positive homogeneous polynomial in the non-singular case.
format article
author Lauret, Jorge Rubén
Oscari, Francisco David
author_facet Lauret, Jorge Rubén
Oscari, Francisco David
author_sort Lauret, Jorge Rubén
title On nonsingular two-step nilpotent Lie algebras
title_short On nonsingular two-step nilpotent Lie algebras
title_full On nonsingular two-step nilpotent Lie algebras
title_fullStr On nonsingular two-step nilpotent Lie algebras
title_full_unstemmed On nonsingular two-step nilpotent Lie algebras
title_sort on nonsingular two-step nilpotent lie algebras
publishDate 2022
url http://hdl.handle.net/11086/30059
https://doi.org/10.48550/arXiv.1209.3060
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bdutipo_str Repositorios
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