Homotopy Maurer-Cartan equation in physics
We consider two approaches for construction of solutions of classical equations of motion that lead to Homotopy Maurer-Cartan equations. In the first approach field variables appear as fluctuations of structure constants of algebra of functions on the manifold. In the second approach equations arise the condition of homotopy conformal invariance near the instantonic background. It is conjectured that the second case is a particular case of the first