Year: 2026
Type: preprint
Abstract: Formal Lie groups, which generalize Lie groups in differential geometry, are analogous to formal group schemes in algebraic geometry. In a previous paper, we established the basic theory of formal Lie groups, including a formal Lie theory theorem that identifies formal Lie groups with Lie pairs. In this paper, we develop the foundations of the representation theory of formal Lie groups and Lie pairs. In particular, we construct modules of Lie pairs on function spaces over formal manifolds and prove that the category of representations of a formal Lie group is isomorphic to the category of modules of the corresponding Lie pair.
Source: arXiv (Cornell University)
Authors: Chen, Fulin, Sun, Binyong, Wang, Chuyun
Institutions: Zhejiang University, Hainan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2791931479
OpenAlex ID: W7213590682