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

2025/02/18 by Edison Alberto Fernández-Culma, Fernández-Culma, Edison Alberto, Nadina Rojas +1
Mathematics · #17B99 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2502.12475

openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the space of Lie algebras equipped with left-invariant complex structures, L_ J_\tinycn (ℝ²ⁿ) , 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 L_ J_\tinycn (ℝ²ⁿ) .

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