Lie's Third Theorem for Lie $\infty$-Algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911509943156736 |
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| author | Rogers, Christopher L. Wolfson, Jesse |
| author_facet | Rogers, Christopher L. Wolfson, Jesse |
| contents | We introduce the theory of local minimal models for Kan simplicial manifolds, which provide the appropriate generalization of minimal Kan simplicial sets to geometric contexts. We use this to obtain the first proof of Lie's third theorem for finite-type Lie $\infty$-algebras: Every finite-type, homologically and non-negatively graded $L_\infty$-algebra over $\mathbb{R}$ integrates to a finite-dimensional Lie $\infty$-group. As a corollary, our construction yields a new explicit finite-dimensional model for the string Lie 2-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lie's Third Theorem for Lie $\infty$-Algebras Rogers, Christopher L. Wolfson, Jesse Rings and Algebras Algebraic Topology Differential Geometry We introduce the theory of local minimal models for Kan simplicial manifolds, which provide the appropriate generalization of minimal Kan simplicial sets to geometric contexts. We use this to obtain the first proof of Lie's third theorem for finite-type Lie $\infty$-algebras: Every finite-type, homologically and non-negatively graded $L_\infty$-algebra over $\mathbb{R}$ integrates to a finite-dimensional Lie $\infty$-group. As a corollary, our construction yields a new explicit finite-dimensional model for the string Lie 2-group. |
| title | Lie's Third Theorem for Lie $\infty$-Algebras |
| topic | Rings and Algebras Algebraic Topology Differential Geometry |
| url | https://arxiv.org/abs/2409.08957 |