XXVIII Workshop on Geometric Methods in Physics | 28.06-04.07.2009 |

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## Theodore Voronov## On a Non-Abelian Poincaré LemmaIt is well known that every Lie algebra valued 1-form satisfying the Maurer-Cartan equation has a logarithmic primitive (locally). I will show how this fact extends to a statement ("Non-Abelian Poincaré Lemma") concerning arbitrary odd forms, possibly inhomogeneous, taking values in a Lie superalgebra. Such a form can be interpreted as Quillen's superconnection. Time permitting, I will explain applications to Lie algebroids and their non-linear analogs. |