2024/01/10 by Dan Aguero, Aguero, Dan
Mathematics · Medicine · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Lipid metabolism and disorders #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2401.05274
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We associate a real distribution to any complex Lie algebroid that we call distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain a real Lie algebroid inside the original complex Lie algebroid. Under another regularity condition, we associate a complex Lie subalgebroid that we call the minimal complex subalgebroid. We also provide a local splitting for complex Lie algebroids with constant real rank. In the last part, we introduce the complex matched pair of skew-algebroids; these pairs produce complex Lie algebroid structures on the complexification of a vector bundle. We use this operation to characterize all the complex Lie algebroid structures on the complexification of real vector bundles.