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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Noncommutative formality implies commutative and Lie formality

Bashar Saleh

Algebraic & Geometric Topology 17 (2017) 2523–2542
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.

Keywords
formality, commutative formality, Lie formality
Mathematical Subject Classification 2010
Primary: 55P62
References
Publication
Received: 10 October 2016
Revised: 1 February 2017
Accepted: 16 February 2017
Published: 3 August 2017
Authors
Bashar Saleh
Department of Mathematics
Stockholm University
SE-106 91 Stockholm
Sweden