Brackets by another name - Whitehead or Samelson products - have a history parallel to that in Kosmann-Schwarzbach's "From Schouten to Mackenzie: notes on brackets". Here I sketch the development of these and some of the other brackets and products and braces within homotopy theory and homological algebra and with applications to mathematical physics. In contrast to the brackets of Schouten, Nijenhuis and of Gerstenhaber, which involve a relation to another graded product, in homotopy theory many of the brackets are free standing binary operations. My path takes me through many twists and turns; unless particularized, bracket will be the generic term including product and brace. The path leads beyond binary to multi-linear $ n $-ary operations, either for a single $ n $ or for whole coherent congeries of such assembled into what is known now as an $ \infty $-algebra, such as in homotopy Gerstenhaber algebras. It also leads to more subtle invariants. Along the way, attention will be called to interaction with 'physics'; indeed, it has been a two-way street.

中文翻译：

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任何其他名称的括号

括号的另一个名称 - Whitehead 或 Samelson 产品 - 与 Kosmann-Schwarzbach 的“从 Schouten 到 Mackenzie：括号注释”中的历史相似。在这里，我概述了同伦理论和同调代数中的这些以及其他一些括号、产品和括号的发展以及在数学物理中的应用。与 Schouten、Nijenhuis 和 Gerstenhaber 的括号（涉及与另一个分级产品的关系）相反，在同伦理论中，许多括号是独立的二元运算。我的道路带我走过许多曲折；除非特别说明，括号将是通用术语，包括产品和支架。这条路径从二元到多线性 $n$-ary 操作，无论是对于单个 $n$ 还是对于这种组装成现在已知的 $\infty$-代数的整个相干集合，例如在同伦 Gerstenhaber代数。它还导致更微妙的不变量。在此过程中，将注意与“物理”的互动；确实，这是一条双向的街道。