Non-commutative formality implies commutative and Lie formality
(English)In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739Article in journal (Refereed) Accepted
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.
formality, commutative formality, Lie formality
Geometry Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-139938OAI: oai:DiVA.org:su-139938DiVA: diva2:1075831