Title

Higher Arity Self-distributive Operations in Cascades and their Cohomology

Document Type

Article

Publication Date

2021

Keywords

Higher arity self-distributive operation, cohomology, internalization

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0219498821501164

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.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Journal of Algebra and Its Applications, v. 20, issue 7, art. 2150116

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