Lie Algebroid Structures on Double Vector Bundles and Representation Theory of Lie Algebroids

Authors

Alfonso Gracia-Saz, University of Toronto
Rajan Amit Mehta, Washington University in St. LouisFollow

Document Type

Article

Publication Date

3-1-2010

Publication Title

Advances in Mathematics

Abstract

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.

Keywords

Characteristic classes, Double category, Lie algebroid, Representation, Superconnection

Volume

223

Issue

4

First Page

1236

Last Page

1275

DOI

10.1016/j.aim.2009.09.010

ISSN

00018708

Rights

© 2009 Elsevier Inc. All rights reserved.

Comments

Archived as published.

Open access article.

Recommended Citation

Gracia-Saz, Alfonso and Mehta, Rajan Amit, "Lie Algebroid Structures on Double Vector Bundles and Representation Theory of Lie Algebroids" (2010). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/93