From Schouten to Mackenzie: notes on brackets

Abstract

In this paper, dedicated to the memory of Kirill Mackenzie, I relate the origins and early development of the theory of graded Lie brackets, first in the publications on differential geometry of Schouten, Nijenhuis, and Frölicher--Nijenhuis, then in the work of Gerstenhaber and Nijenhuis--Richardson in cohomology theory.

To appear in the special issue of the Journal of Geometric Mechanics in memory of Kirill Mackenzie