Deformations of Linear Lie Brackets

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.

32 pages, comments welcome! Accepted for publication in Pacific J. Math

References in corpus (3)

• Supergroupoids, double structures, and equivariant cohomology
• $Q$-Manifolds and Mackenzie Theory
• Deformation Cohomology of Lie Algebroids and Morita Equivalence

Cited by in corpus (4)

• Multiplicative Connections and Their Lie Theory
• Fiber-Wise Linear Differential Operators
• Gauge equivalences for foliations and pre-symplectic structures
• Almost Commutative Q-algebras and Derived brackets