Double Lie Algebroids and Representations up to Homotopy

Authors

A. Gracia-Saz, University of Toronto
M. Jotz Lean, The University of Sheffield
K. C. H. Mackenzie, The University of Sheffield
Rajan Amit Mehta, Smith CollegeFollow

Document Type

Article

Publication Date

6-2018

Publication Title

Journal of Homotopy and Related Structures

Abstract

We show that a double Lie algebroid, together with a chosen decomposition, is equivalent to a pair of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the double Lie algebroids arising from the tangent bundle of a Lie algebroid and the cotangent bundle of a Lie bialgebroid.

Keywords

Double Lie algebroids, Representations up to homotopy, Matched pairs

Volume

13

Issue

2

First Page

287

Last Page

319

DOI

doi.org/10.1007/s40062-017-0183-1

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Comments

Archived as published.

Recommended Citation

Gracia-Saz, A.; Lean, M. Jotz; Mackenzie, K. C. H.; and Mehta, Rajan Amit, "Double Lie Algebroids and Representations up to Homotopy" (2018). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/41