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Non-commutative formality implies commutative and Lie formality
Stockholm University, Faculty of Science, Department of Mathematics.
(English)In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739Article in journal (Refereed) Accepted
Abstract [en]

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.

Keyword [en]
formality, commutative formality, Lie formality
National Category
Geometry Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-139938OAI: oai:DiVA.org:su-139938DiVA: diva2:1075831
Available from: 2017-02-21 Created: 2017-02-21 Last updated: 2017-09-03Bibliographically approved

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