Lie algebroid modules and representations up to homotopy

2011/07/31 by Rajan Amit Mehta · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #math.DG #msc:16E45 #msc:53D17 #msc:58A50

paper · pdf · doi:10.1016/j.indag.2014.07.013

published as Indagationes Mathematicae 25 (2014), no. 5, 1122-1134 · v3: Final version, to appear in Indag. Math

openalex publication_date 2014/07/16 · arxiv created 2014/09/08 · arxiv updated 2015/01/27 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

Abstract

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaintrob's Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.

Citations

• Courant algebroids, derived brackets and even symplectic supermanifolds
• Supergroupoids, double structures, and equivariant cohomology
• Transverse measures, the modular class and a cohomology pairing for Lie algebroids
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes

Cited by

• L_∞-actions of Lie algebroids