Higher Arity Self-Distributive Operations in Cascades and their Cohomology

Mohamed Elhamdadi; Masahico Saito; Emanuele Zappala

doi:10.1142/s0219498821501164

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arXiv · 1905.00440

Higher Arity Self-Distributive Operations in Cascades and their Cohomology

Mohamed Elhamdadi·Masahico Saito·Emanuele Zappala

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Abstract

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.

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Mohamed Elhamdadi, Masahico Saito, Emanuele Zappala. 2019-05-01. Higher Arity Self-Distributive Operations in Cascades and their Cohomology. https://doi.org/10.1142/s0219498821501164

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