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Homotopical Algebra for Lie Algebroids
Applied Categorical Structures ( IF 0.6 ) Pub Date : 2019-02-18 , DOI: 10.1007/s10485-019-09563-z
Joost Nuiten

We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $$L_\infty $$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.

中文翻译:

李代数的同伦代数

我们在特征零的可交换 dg-代数上,在 dg-Lie 代数和 $$L_\infty $$L∞-代数的类别上构造 Quillen 等效半模型结构。这允许人们将同伦代数的常用方法应用于 dg-Lie 代数体:例如,每个 Lie 代数体都可以通过 dg-Lie 代数产生的 dg-Lie 代数体来解决,即其锚映射为零。作为一个应用,我们展示了李代数上同调如何由 dg-李代数同伦范畴中的对象表示。
更新日期:2019-02-18
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