VB-algebroid morphisms and representations up to homotopy

Thiago Drummond; Madeleine Jotz Lean; Cristian Ortiz

doi:10.1016/j.difgeo.2015.03.005

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arXiv · 1302.3987

VB-algebroid morphisms and representations up to homotopy

Thiago Drummond·Madeleine Jotz Lean·Cristian Ortiz

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Abstract

We show in this paper that the correspondence between $2$-term representations up to homotopy and $\mathcal{VB}$-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 $A$.

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Thiago Drummond, Madeleine Jotz Lean, Cristian Ortiz. 2016-02-22. VB-algebroid morphisms and representations up to homotopy. https://doi.org/10.1016/j.difgeo.2015.03.005

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