Volume 17, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
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