2020/11/30 by Malte Heuer, Heuer, Malte, Madeleine Jotz Lean +1
Mathematics · Physics and Astronomy · #32L05 #53B05 #53D17 (Secondary) #53D18 (Primary) #58A50 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2011.14652
openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle E→ M is equivalent to a \mathbb C-multiplication j in the fibers of TM⊕ E^* and \mathbb C-Lie algebroid structure on TM⊕ E^*. Generalised complex Lie algebroids (or Glanon algebroids) are then studied in this context, and expressed as a pair of complex conjugated Lie bialgebroids.