2006/01/31 by A. J. Weinstein, Alan Weinstein, Weinstein, Alan · 2 citations
Computer Science · Mathematics · #32Q99 #58H05 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation #math.DG #msc:32Q99 #msc:58H05
paper · pdf · doi:10.48550/arxiv.math/0601752
21 pages
arxiv created 2006/01/31 · openalex publication_date 2006/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a complexification of M and integration to a holomorphic groupoid. A collection of diverse examples reveal that the holomorphic stacks presented by these groupoids tend to coincide with known objects associated to structures in complex geometry. This suggests that the object integrating a complex Lie algebroid should be a holomorphic stack.