Covariance in the Batalin-Vilkovisky formalism and the Maurer-Cartan equation for curved Lie algebras

We express covariance of the Batalin-Vilkovisky formalism in classical mechanics by means of the Maurer-Cartan equation in a curved Lie superalgebra, defined using the formal variational calculus and Sullivan’s Thom-Whitney construction. We use this framework to construct a Batalin-Vilkovisky canonical transformation identifying the Batalin-Vilkovisky formulation of the spinning particle with an AKSZ field theory.