Non-commutative formality implies commutative and Lie formality
Algebraic Topology
2018-03-16 v2 K-Theory and Homology
Quantum Algebra
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.
Cite
@article{arxiv.1609.02540,
title = {Non-commutative formality implies commutative and Lie formality},
author = {Bashar Saleh},
journal= {arXiv preprint arXiv:1609.02540},
year = {2018}
}
Comments
Final version. To appear in Algebraic & Geometric Topology