QP-structures of degree 3 and CLWX 2-algebroids
Differential Geometry
2020-02-28 v3 Mathematical Physics
math.MP
Abstract
In this paper, we give the notion of a CLWX 2-algebroid and show that a QP-structure of degree 3 gives rise to a CLWX 2-algebroid. This is the higher analogue of the result that a QP-structure of degree 2 gives rise to a Courant algebroid. A CLWX 2-algebroid can also be viewed as a categorified Courant algebroid. We show that one can obtain a Lie 3-algebra from a CLWX 2-algebroid. Furthermore, CLWX 2-algebroids are constructed from split Lie 2-algebroids and split Lie 2-bialgebroids.
Keywords
Cite
@article{arxiv.1602.01127,
title = {QP-structures of degree 3 and CLWX 2-algebroids},
author = {Jiefeng Liu and Yunhe Sheng},
journal= {arXiv preprint arXiv:1602.01127},
year = {2020}
}
Comments
27 pages, notations are changed, we use the terminology "CLWX 2-algebroid" instead of "LWX 2-algebroid", the construction of a transformation CLWX 2-algebroid is given, to appear in J. Symplectic Geometry