Noncommutative formality implies commutative and Lie formality

Saleh, Bashar

doi:10.2140/agt.2017.17.2523

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Noncommutative formality implies commutative and Lie formality

Bashar Saleh

Algebraic & Geometric Topology 17 (2017) 2523–2542

DOI: 10.2140/agt.2017.17.2523

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

Volume 17, issue 4 (2017)