2014/09/02 by Nicolás Martínez Alba, Alba, Nicolas Martinez
Mathematics · #53D17 #53D20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1409.0695
openalex publication_date 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce poly-symplectic groupoids, which are natural extensions of symplectic groupoids to the context of poly-symplectic geometry, and define poly-Poisson structures as their infinitesimal counterparts. We present equivalent descriptions of poly-Poisson structures, including one related with AV-Dirac structures. We also discuss symmetries and reduction in the setting of poly-symplectic groupoids and poly-Poisson structures, and use our viewpoint to revisit results and develop new aspects of the theory initiated by D.Iglesias, J.C Marrero and M. Vaquero.