Koszul duality and the Poincar\'e-Birkhoff-Witt theorem
| Autor: | Getzler, Ezra |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $UL$. Comment: 26 pages. Some misprints corrected |
| Databáze: | arXiv |
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