Based on results of Vallette [Val14], we endow the category of conilpotent Lie coalgebras with a model structure. 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 relationships of this procedure with existing literature, namely the works of Lazarev–Markl and Buijs–Félix–Murillo–Tanré.
Received: March 13, 2018
Published online: August 05, 2018
Daniel Robert-NicoudLaboratoire Analyse, Géométrie et Applications,
Université Paris 13, Sorbonne Paris Cité,
99 Avenue Jean Baptiste Clément,
93430 Villetaneuse, France.