2022/10/31 by Daniel Álvarez · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.DG #math.SG
paper · pdf · doi:10.1093/imrn/rnad265
published as Int. Math. Res. Not. IMRN 2024 (9), (2024), 7526-7551 · v4: Final version, minor corrections
openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · arxiv created 2026/07/29 · openalex updated_date 2026/07/29 · arxiv updated 2026/07/30
Abstract In this work, we extend the Lu–Weinstein construction of double symplectic groupoids to any Lie bialgebroid such that its associated Courant algebroid is transitive and its Atiyah algebroid integrable. We illustrate this result by showing how it generalises many of the examples of double symplectic groupoids that have appeared in the literature. As preliminary steps for this construction, we give a classification of exact twisted Courant algebroids over Lie groupoids (CA-groupoids for short) and we show the existence of a foliation by twisted Courant algebroids on the base of a twisted CA-groupoid.