A model structure for the Goldman-Millson theorem

Abstract

By a result of Vallette, we put a sensible model structure on the category of conilpotent Lie coalgebras. This gives us a powerful tool to study the subcategory of Lie algebras obtained by linear dualization, also known as the category of pronilpotent Lie algebras. This way, we recover weaker versions of the celebrated Goldman-Millson theorem and Dolgushev-Rogers theorem by purely homotopical methods. We explore the relations of this procedure with the existent literature, namely the works of Lazarev-Markl and Buijs-Félix-Murillo-Tanré.

20 pages. (v2) fixed formatting of abstract on arXiv, the core text was not touched

References in corpus (9)

• Lie theory for nilpotent L-infinity algebras
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Representing the deformation $\infty$-groupoid
• Homotopy theory of complete Lie algebras and Lie models of simplicial sets
• A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras
• Descent of Deligne-Getzler $\infty$-groupoids
• The infinity Quillen functor, Maurer-Cartan elements and DGL realizations
• Deformation theory with homotopy algebra structures on tensor products
• MC Elements in Pronilpotent DG Lie Algebras

Cited by in corpus (2)

• Convolution algebras and the deformation theory of infinity-morphisms
• Gauge equivalence for complete $L_{\infty }$-algebras