𝑁-flat connections

Abstract

We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth N on an affine manifold, and N -flat covariant derivatives.

On the (3, N ) Maurer-Cartan equation

“…A N -differential graded algebra A consist of a Z-graded associative algebra A = n∈Z A n together with a degree The main question regarding this definition is whether there are interesting examples of N -differential graded algebras. Much work still needs to be done, but already a variety of examples has been constructed in [4,5]. These examples may be classified as follows:…”

“…The study of the deformations of the differential of a N-dga has also been initiated in [2]. Applications to differential geometry are given in [3]. Applications to the study of A ∞ -algebras of depth N, are contained in [4].…”