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An elementary approach to the model structure on DG-Lie algebras
- Source :
- Rendiconti di Matematica e delle Sue Applicazioni, Vol 44, Iss 1-2, Pp 53-76 (2023)
- Publication Year :
- 2023
- Publisher :
- Sapienza Università Editrice, 2023.
-
Abstract
- This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions, which are particularly nice cofibrations. The cobar construction of a locally conilpotent cocommutative coalgebra is shown to be an example of semifree DG-Lie algebra. We also give an example of a non-cofibrant DG-Lie algebra whose underlying graded Lie algebra is free; this cannot occur in the bounded above case, where DG-Lie algebras of this form are always cofibrant.
Details
- Language :
- English, French, Italian
- ISSN :
- 11207183 and 25323350
- Volume :
- 44
- Issue :
- 1-2
- Database :
- Directory of Open Access Journals
- Journal :
- Rendiconti di Matematica e delle Sue Applicazioni
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.4f0f2c54169c48f2863bb9725a862cba
- Document Type :
- article