Vol. 303, No. 1, 2019

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Deformations of linear Lie brackets

Pier Paolo La Pastina and Luca Vitagliano

Vol. 303 (2019), No. 1, 265–298

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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Lie algebroids, VB-algebroids, deformations, graded manifolds, deformation cohomology
Mathematical Subject Classification 2010
Primary: 22A22, 58H05, 58H15
Secondary: 17B55
Received: 4 June 2018
Revised: 1 March 2019
Accepted: 2 March 2019
Published: 21 December 2019
Pier Paolo La Pastina
Department of Mathematics
Sapienza University of Rome
Luca Vitagliano
Department of Mathematics
University of Salerno