Noncommutative formality implies commutative and Lie formality

Saleh, Bashar¹

¹Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden

Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2523-2542

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.2523

Classification : 55P62
Keywords: formality, commutative formality, Lie formality

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