From Schouten to Mackenzie: notes on brackets

2021/05/31 by Yvette Kosmann–Schwarzbach, Kosmann-Schwarzbach, Yvette
Mathematics · #16E40 #17-03 #53-03 #53C15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #History and Overview (math.HO) #Homotopy and Cohomology in Algebraic Topology #Primary: 01A60 #Rings and Algebras (math.RA) #Secondary: 17B70

paper · pdf · doi:10.48550/arxiv.2105.14828

openalex publication_date 2021/05/31 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

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.

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