Deformations of Linear Lie Brackets
Differential Geometry
2019-12-25 v2 Representation Theory
Symplectic Geometry
Abstract
A VB-algebroid is a vector bundle object in the category of Lie algebroids. We attach to every VB-algebroid a differential graded Lie algebra and we show that it controls deformations of the VB-algebroid structure. Several examples and applications are discussed. This is the first in a series of papers devoted to deformations of vector bundles and related structures over differentiable stacks.
Cite
@article{arxiv.1805.02108,
title = {Deformations of Linear Lie Brackets},
author = {Pier Paolo La Pastina and Luca Vitagliano},
journal= {arXiv preprint arXiv:1805.02108},
year = {2019}
}
Comments
32 pages, comments welcome! Accepted for publication in Pacific J. Math