Higher Poincare Lemma and Integrability

Getachew Alemu Demessie; Christian Saemann

doi:10.1063/1.4929537

Higher Poincare Lemma and Integrability

Getachew Alemu Demessie, Christian Saemann

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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Abstract

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat local connective structure to the trivial one. Finally, we show how higher flatness appears as a necessary integrability condition of a linear system which featured in recently developed twistor descriptions of higher gauge theories.

Original language	English
Article number	082902
Journal	Journal of Mathematical Physics
Volume	56
Issue number	8
DOIs	https://doi.org/10.1063/1.4929537
Publication status	Published - 28 Aug 2015

Keywords

hep-th
math-ph
math.DG
math.MP

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10.1063/1.4929537

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Copyright (2015) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in ( Journal of Mathematical Physics 56, 082902 (2015); doi: 10.1063/1.4929537) and may be found at (http://dx.doi.org/10.1063/1.4929537).
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Higher Poincare Lemma and Integrability

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