On the variety of Lie algebras endowed with complex structures: degenerations and deformations.

IF 0.8 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2026-03-13 DOI:10.1007/s10455-026-10034-7

Edison Alberto Fernández-Culma, Nadina Rojas

引用次数: 0

Abstract

We study the space of Lie algebras equipped with left-invariant complex structures, \( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \), with particular attention to their degenerations and deformations. To this end, we identify certain invariants that remain well-behaved under degenerations while preserving the complex structure. These concepts are then applied to the four-dimensional case. Additionally, we explore applications to the study of left-invariant Hermitian structures on Lie groups, and we discuss some aspects of the deformation theory within \( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \).

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具有复杂结构的李代数的多样性：退化和变形。

我们研究了具有左不变复结构（\( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \)）的李代数空间，特别注意了它们的退化和变形。为此，我们确定了在退化下保持良好行为同时保留复杂结构的某些不变量。然后将这些概念应用于四维情况。此外，我们探讨了在李群上左不变厄米结构研究中的应用，并在\( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \)中讨论了变形理论的一些方面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.