Integration of 2-term representations up to homotopy via 2-functors

Cristian Ortiz; Olivier Brahic

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arXiv · 1608.00664

Integration of 2-term representations up to homotopy via 2-functors

Cristian Ortiz·Olivier Brahic

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Abstract

Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated to a representation up to homotopy. As applications, we describe alternative integration schemes for semi-direct products of Lie 2-algebras and string algebras.

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BibTeX RIS

Cristian Ortiz, Olivier Brahic. 2016-08-02. Integration of 2-term representations up to homotopy via 2-functors. https://arxiv.org/abs/1608.00664

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