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.File allegati a questo prodotto
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