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- Title
Higher arity self-distributive operations in Cascades and their cohomology.
- Authors
Elhamdadi, Mohamed; Saito, Masahico; Zappala, Emanuele
- 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.
- Subjects
COHOMOLOGY theory; HOPF algebras; LIE algebras; LABELING theory; COCYCLES
- Publication
Journal of Algebra & Its Applications, 2021, Vol 20, Issue 7, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498821501164