Homotopical algebra for Lie algebroids
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866914767158902784 |
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| author | Nuiten, Joost |
| author_facet | Nuiten, Joost |
| contents | We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $L_\infty$-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra to dg-Lie algebroids: for example, every Lie algebroid can be resolved by dg-Lie algebroids that arise from dg-Lie algebras, i.e. that have a null-homotopic anchor map. As an application, we show how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_03441 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Homotopical algebra for Lie algebroids Nuiten, Joost Algebraic Topology Category Theory We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $L_\infty$-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra to dg-Lie algebroids: for example, every Lie algebroid can be resolved by dg-Lie algebroids that arise from dg-Lie algebras, i.e. that have a null-homotopic anchor map. As an application, we show how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids. |
| title | Homotopical algebra for Lie algebroids |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/1712.03441 |