Homotopical Algebra for Lie Algebroids

Joost Nuiten*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)493-534
Number of pages42
JournalApplied Categorical Structures
Volume27
Issue number5
DOIs
Publication statusPublished - 1 Oct 2019

Keywords

  • Dg-Lie algebroid
  • Lie algebroid cohomology
  • Model category

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