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.

Deformations of linear Lie brackets / LA PASTINA, PIER PAOLO; Vitagliano, Luca. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - 303-1:(2019), pp. 265-298. [10.2140/pjm.2019.303.265]

Deformations of linear Lie brackets

Pier Paolo La Pastina;Luca Vitagliano
2019

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.
2019
deformations vb algebroids
01 Pubblicazione su rivista::01a Articolo in rivista
Deformations of linear Lie brackets / LA PASTINA, PIER PAOLO; Vitagliano, Luca. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - 303-1:(2019), pp. 265-298. [10.2140/pjm.2019.303.265]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1343250
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