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From Schouten to Mackenzie: Notes on brackets

In Memory of Kirill Mackenzie (1951–2020)

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  • 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.

    Mathematics Subject Classification: Primary: 01A60, 17-03, 53-03; Secondary: 17B70, 16E40, 53C15.


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    [28] J. A. Schouten, Sur les tenseurs de $V^{n}$ aux directions principales $V^{n-1}$-normales, in Colloque Géom. diff., Louvain 1951, Georges Thone, Liège; Masson & Cie, Paris (1951), 67–70.
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    [35] A. Tonolo, Sopra una classe di deformazioni finite, Ann. Mat. Pura Appl., Ⅳ. Ser., 29 (1949), 99–114. doi: 10.1007/BF02413917.
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