Non-commutative formality implies commutative and Lie formality

Abstract

Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg associative algebra if and only if it is formal as a commutative dg algebra. We present some consequences of these theorems in rational homotopy theory.

Final version. To appear in Algebraic & Geometric Topology

Cited by in corpus (5)

• Cohomology of generalized configuration spaces
• Etale cohomology, purity and formality with torsion coefficients
• Equivariant formality of istropy actions
• Higher structures in rational homotopy theory
• E2 formality via obstruction theory