Ad-invariant metrics on nonnice nilpotent Lie algebras

被引：0

作者：

Conti, D. ^{[1
]}

del Barco, V. ^{[2
]}

Rossi, F. A. ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 6, I-56127 Pisa, Italy

[2] Univ Estadual Campinas, Inst Matemat Estat & Computcao Cient, Rua Sergio Buarque Holanda 651,Cidade Univ Zeferin, BR-13083859 Campinas, SP, Brazil

[3] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年 / 24卷 / 10期

基金：

巴西圣保罗研究基金会;

关键词：

Ad-invariant metric; nice Lie algebra; free nilpotent Lie algebra;

D O I：

10.1142/S0219498825502329

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：26

共 27 条

[1]

Bajo I., Benayadi S., Lie algebras with quadratic dimension equal to 2, J. Pure Appl. Algebra, 209, 3, pp. 725-737, (2007)

[2]

Baum H., Kath I., Doubly extended Lie groups curvature, holonomy and parallel spinors, Differ. Geom. Appl, 19, 3, pp. 253-280, (2003)

[3]

Benito P., de-la-Concepcion D., An overview of free nilpotent Lie algebras, Comment, Math. Univ. Carol, 55, 3, pp. 325-339, (2014)

[4]

Conti D., DEMONbLAST, a program to compute Diagonal Einstein Metrics On Nice Lie Algebras of Surjective Type

[5]

Conti D., Gleipnir, a program to study the Nikolayevsky derivation on Lie algebras with a parameter

[6]

Conti D., del Barco V., Rossi F. A., Uniqueness of ad-invariant metrics, Tohoku Math. J. To appear, (2021)

[7]

Conti D., Rossi F. A., Construction of nice nilpotent Lie groups, J. Algebra, 525, pp. 311-340, (2019)

[8]

Conti D., Rossi F. A., Nice pseudo-Riemannian nilsolitons, J. Geom. Phys, 173, (2022)

[9]

del Barco V., Ovando G. P., Free nilpotent Lie algebras admitting ad-invariant metrics, J. Algebra, 366, pp. 205-216, (2012)

[10]

del Barco V., Ovando G. P., Vittone F., On the isometry groups of invariant Lorentzian metrics on the Heisenberg group, Mediterr. J. Math, 11, 1, pp. 137-153, (2014)

← 1 2 3 →