VB-algebroid morphisms and representations up to homotopy

2013/02/28 by Thiago Drummond, Madeleine Jotz Lean, Cristian Ortiz · 1 citation
Mathematics · #math.DG #math.RT

paper · pdf · doi:10.1016/j.difgeo.2015.03.005

published as Differential Geometry and its Applications 40 (2015): 332-357

arxiv created 2016/02/22 · arxiv updated 2016/02/23

Abstract

We show in this paper that the correspondence between 2-term representations up to homotopy and VB-algebroids, established by Gracia-Saz and Mehta, holds also at the level of morphisms. This correspondence is hence an equivalence of categories. As an application, we study foliations and distributions on a Lie algebroid, that are compatible both with the linear structure and the Lie algebroid structure. In particular, we show how infinitesimal ideal systems in a Lie algebroid A are related with subrepresentations of the adjoint representation of A.

Cited by

• Homotopy of representations up to homotopy

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