Lie algebroid modules and representations up to homotopy

Authors

Rajan Amit Mehta, Smith CollegeFollow

Document Type

Article

Publication Date

10-2014

Publication Title

Indagationes Mathematicae

Abstract

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’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.

Keywords

Lie algebroid, Representation up to homotopy, Graded manifold, Graded vector bundle, Q-manifold

Volume

25

Issue

5

First Page

1122

Last Page

1134

DOI

dx.doi.org/10.1016/j.indag.2014.07.013

ISSN

0019-3577

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit, "Lie algebroid modules and representations up to homotopy" (2014). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/15