Maurer-Cartan spaces of filtered L-infinity algebras

Abstract

We study several homotopical and geometric properties of Maurer-Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras play a key role especially in the deformation theory of algebraic structures. In particular, we prove that the Maurer-Cartan simplicial set preserves fibrations and quasi-isomorphisms. Then we present an algebraic geometry viewpoint on Maurer-Cartan moduli sets, and we compute the tangent complex of the associated algebraic stack.

27 pages, minor corrections and reference added. To appear in JHRS

References in corpus (2)

• Deformation theory and rational homotopy type
• A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras

Cited by in corpus (2)

• Lectures on shifted Poisson geometry
• 1-minimal models for $C_{\infty }$-algebras and flat connections