2025/10/14 by Pelletier, Fernand, Cabau, Patrick
#22A22 #22E65 #46T05 #57R2 #70G45 #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2510.12688
The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how an adapted notion of "bi-algebroid " in finite dimension (cf. \citeMaXu94) can be, nevertheless, recovered. This paper is self-contained and recalls some important properties of "partial Poisson manifolds" (cf. \citeCaPe23, Chapter~7) and "Banach Poisson Lie groups" (cf. \citeTum20) needed for their purpose. The paper also gives an illustration of these concepts from all the results of A.~Odzijewicz and his collaborators on Lie groupoids and Von Neumann algebras.