Involution algebroids: a generalisation of Lie algebroids for tangent categories
Category Theory
2019-05-14 v3 Differential Geometry
Abstract
We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to the Yang-Baxter equation. Every classical Lie algebroid has the structure of an involution algebroid and every involution algebroid in a tangent category admits a Lie bracket on the sections of its underlying bundle. As an illustrative application we take the first steps in developing the homotopy theory of involution algebroids.
Keywords
Cite
@article{arxiv.1904.06594,
title = {Involution algebroids: a generalisation of Lie algebroids for tangent categories},
author = {Matthew Burke and Benjamin MacAdam},
journal= {arXiv preprint arXiv:1904.06594},
year = {2019}
}