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arXiv · 1712.03441

Homotopical algebra for Lie algebroids

Joost Nuiten
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Abstract

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.

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Joost Nuiten. 2017-12-09. Homotopical algebra for Lie algebroids. https://doi.org/10.1007/s10485-019-09563-z

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