Homotopical Algebra for Lie Algebroids
Publication date
2019-10-01
Authors
Nuiten, J.J.
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Article
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taverne
Abstract
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and L∞-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. whose anchor map is zero. As an application, we show how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids.
Keywords
Dg-Lie algebroid, Lie algebroid cohomology, Model category, Taverne, Theoretical Computer Science, General Computer Science
Citation
Nuiten, J 2019, 'Homotopical Algebra for Lie Algebroids', Applied Categorical Structures, vol. 27, no. 5, pp. 493-534. https://doi.org/10.1007/s10485-019-09563-z