Higher braces via formal (non)commutative geometry

We translate the main result of author's arXiv:1309.7744 to the language of formal geometry. In this new setting we prove directly that the Koszul resp. Borjeson braces are pullbacks of linear vector fields over the formal automorphism exp(a) -1 in the Koszul, resp. a/(1-a) in the Borjeson case. We then argue that both braces are versions of the same object, once materialized in the world of formal commutative geometry, once in the non-commutative one.