We investigate constructions of higher arity self-distributive operations, and give relations between cohomology groups corresponding to operations of different arities. For this purpose we introduce the notion of mutually distributive n-ary operations generalizing those for the binary case, and define a cohomology theory labeled by these operations. A geometric interpretation in terms of framed links is described, with the scope of providing algebraic background of constructing 2-cocycles for framed link invariants. This theory is also studied in the context of symmetric monoidal categories. Examples from Lie algebras, coalgebras and Hopf algebras are given.

中文翻译：

---

级联中的高元自分配运算及其上同调

我们研究了更高元自分配运算的构造，并给出了对应于不同元运算的上同调群之间的关系。为此，我们引入了相互分配的概念n元运算概括了二元情况的运算，并定义了由这些运算标记的上同调理论。描述了根据框架链接的几何解释，并提供了构建的代数背景2-cocycles 用于框架链接不变量。该理论也在对称幺半群范畴的背景下进行了研究。给出了李代数、余代数和 Hopf 代数的例子。