A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras

Abstract

In this paper we consider $L_{\infty }$-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an $L_{\infty }$ quasi-isomorphism $U:L\to \tilde{L}$ induces a weak equivalence between the Deligne-Getzler-Hinich (DGH) $\infty$-groupoids corresponding to $L$ and $\tilde{L}$, respectively. This paper may be considered as a modest addition to foundational paper arXiv:math/0404003 by Ezra Getzler.

arXiv commentThe final version will appear in the Journal of Algebra. Comments are still welcome

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Cited by in corpus (5)

• Convolution algebras and the deformation theory of infinity-morphisms
• A model structure for the Goldman-Millson theorem
• Maurer-Cartan spaces of filtered L-infinity algebras
• A Variation of the Goldman-Millson Theorem for Filtered $L_{\infty }$ Algebras
• Towards deformation quantization over a Z-graded base