Koszul duality and the Poincaré–Birkhoff–Witt theorem
Year: 2025
Type: article
Abstract: Using a homotopy introduced by de Wilde and Lecomte and homological perturbation theory for A_{\infty} -algebras, we give an explicit proof that the universal enveloping algebra UL of a differential graded Lie algebra L is Koszul, via an explicit contracting homotopy from the cobar construction \Omega CL of the Chevalley–Eilenberg chain coalgebra CL of L to UL . This may be viewed as an extension of the Poincaré–Birkhoff–Witt theorem to L_{\infty} -algebras.
Source: L’Enseignement Mathématique
DOI: 10.4171/lem/1098
Author: Ezra Getzler
Institution: Northwestern University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414424906
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