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Abstract
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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.
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Keywords
Lie algebroids, VB-algebroids, deformations, graded
manifolds, deformation cohomology
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Mathematical Subject Classification 2010
Primary: 22A22, 58H05, 58H15
Secondary: 17B55
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Milestones
Received: 4 June 2018
Revised: 1 March 2019
Accepted: 2 March 2019
Published: 21 December 2019
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