Lie's Third Theorem for Lie $\infty$-Algebras

Christopher L. Rogers; Jesse Wolfson

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arXiv · 2409.08957

Lie's Third Theorem for Lie $\infty$-Algebras

Christopher L. Rogers·Jesse Wolfson

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Abstract

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.

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BibTeX RIS

Christopher L. Rogers, Jesse Wolfson. 2024-09-13. Lie's Third Theorem for Lie $\infty$-Algebras. https://arxiv.org/abs/2409.08957

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