Lie algebroid modules and representations up to homotopy

Citation data:

Indagationes Mathematicae, ISSN: 0019-3577, Vol: 25, Issue: 5, Page: 1122-1134

Publication Year:
2014
Usage 61
Downloads 58
Abstract Views 3
Captures 1
Exports-Saves 1
Citations 5
Citation Indexes 5
Repository URL:
https://scholarworks.smith.edu/mth_facpubs/15; http://arxiv.org/abs/1107.1539
DOI:
10.1016/j.indag.2014.07.013
Author(s):
Mehta, Rajan Amit
Publisher(s):
Elsevier BV
Tags:
Mathematics; Lie algebroid; Representation up to homotopy; Graded manifold; Graded vector bundle; Q-manifold; Mathematics - Differential Geometry; 16E45, 53D17, 58A50
article description
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.