Abstract
We propose a new general formalism that allows us to study Poincaré–Birkhoff–Witt type phenomena for universal enveloping algebras in the differential graded context. Using it, we prove a homotopy invariant version of the classical Poincaré–Birkhoff–Witt theorem for universal envelopes of Lie algebras. In particular, our results imply that all the previously known constructions of universal envelopes of L∞-algebras (due to Baranovsky, Lada and Markl, and Moreno-Fernández) represent the same object of the homotopy category of differential graded associative algebras. We also extend Quillen’s classical quasi-isomorphism C⟶ BU from differential graded Lie algebras to L∞-algebras; this confirms a conjecture of Moreno-Fernández.
Original language | English |
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Article number | 15 |
Journal | Letters in Mathematical Physics |
Volume | 113 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2023 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
Keywords
- Algebraic operads
- Homotopical algebra
- L -algebras
- Universal enveloping algebras
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics