From Schouten to Mackenzie: notes on brackets
Yvette Kosmann-Schwarzbach
TL;DR
This paper traces the historical development of graded Lie brackets from early differential geometry to their role in cohomology theory, highlighting key contributions and evolutions in the field.
Contribution
It provides a detailed historical analysis of the origins and development of graded Lie brackets, connecting foundational work across different mathematical disciplines.
Findings
Highlights the progression from Schouten's work to Mackenzie's contributions.
Connects early geometric brackets to cohomological applications.
Emphasizes the influence of key mathematicians in the evolution of the theory.
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 Fr\"olicher--Nijenhuis, then in the work of Gerstenhaber and Nijenhuis--Richardson in cohomology theory.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models