Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909846105751552 |
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| author | Pelletier, Fernand Cabau, Patrick |
| author_facet | Pelletier, Fernand Cabau, Patrick |
| contents | 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. \cite{MaXu94}) can be, nevertheless, recovered. This paper is self-contained and recalls some important properties of "partial Poisson manifolds" (cf. \cite{CaPe23}, Chapter~7) and "Banach Poisson Lie groups" (cf. \cite{Tum20}) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras Pelletier, Fernand Cabau, Patrick Differential Geometry Operator Algebras 22A22, 22E65, 46T05, 57R2, 70G45 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. \cite{MaXu94}) can be, nevertheless, recovered. This paper is self-contained and recalls some important properties of "partial Poisson manifolds" (cf. \cite{CaPe23}, Chapter~7) and "Banach Poisson Lie groups" (cf. \cite{Tum20}) 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. |
| title | Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras |
| topic | Differential Geometry Operator Algebras 22A22, 22E65, 46T05, 57R2, 70G45 |
| url | https://arxiv.org/abs/2510.12688 |