Koszul duality and the Poincaré-Birkhoff-Witt theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909677847052288 |
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| author | Getzler, Ezra |
| author_facet | Getzler, Ezra |
| contents | 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 $ΩCL$ of the Chevalley-Eilenberg chain coalgebra $CL$ of $L$ to $UL$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koszul duality and the Poincaré-Birkhoff-Witt theorem Getzler, Ezra K-Theory and Homology 16E40 (Primary) 13D03, 16S37, 17B35 (Secondary) 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 $ΩCL$ of the Chevalley-Eilenberg chain coalgebra $CL$ of $L$ to $UL$. |
| title | Koszul duality and the Poincaré-Birkhoff-Witt theorem |
| topic | K-Theory and Homology 16E40 (Primary) 13D03, 16S37, 17B35 (Secondary) |
| url | https://arxiv.org/abs/2405.14798 |