Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure

2003/10/13 by Novica Blažić, N. Blazic, Blazic, N. +3
Mathematics · Physics and Astronomy · #32M10 #53C26 #53C50 #53C55 #53C56 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:32M10 #msc:53C26 #msc:53C50 #msc:53C55 #msc:53C56

paper · pdf · doi:10.48550/arxiv.math/0310180

15 pages

arxiv created 2003/10/13 · openalex publication_date 2003/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main goal is to classify 4-dimensional real Lie algebras \g which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore possessing a neutral, left-invariant, anti-self-dual metric. Our study is related to the work of Barberis who classified real, 4-dimensional simply-connected Lie groups which admit an invariant hypercomplex structure.

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