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arXiv · 1506.00048

The Role of the Jacobi Identity in Solving the Maurer-Cartan Structure Equation

Ori Yudilevich
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Abstract

We describe a method for solving the Maurer-Cartan structure equation associated with a Lie algebra that isolates the role of the Jacobi identity as an obstruction to integration. We show that the method naturally adapts to two other interesting situations: local symplectic realizations of Poisson structures, in which case our method sheds light on the role of the Poisson condition as an obstruction to realization; and the Maurer-Cartan structure equation associated with a Lie algebroid, in which case we obtain an explicit formula for a solution to the equation which generalizes the well known formula in the case of Lie algebras.

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Ori Yudilevich. 2015-05-29. The Role of the Jacobi Identity in Solving the Maurer-Cartan Structure Equation. https://doi.org/10.2140/pjm.2016.282.487

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