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
Scholar Commons Citation
Elhamdadi, Mohamed; Saito, Masahico; and Zappala, Emanuele, "Higher Arity Self-distributive Operations in Cascades and their Cohomology" (2021). Mathematics and Statistics Faculty Publications. 90.
https://digitalcommons.usf.edu/mth_facpub/90
