Higher-Arity Structures

Ternary algebras, such as semiheaps and 3-Lie algebras, are investigated for their purely mathematical properties and the potential to generalize the notion of symmetry in physical theories. This line of research works towards the resolution of long-standing open problems in algebra, such as the integration of n-Leibniz algebras, which can lead to insights in the generalization of gauge theories and, in particular, a better understanding of the strong nuclear force.

More generally, based on the diagrammatic approach to category theory, the extension of morphisms to higher-arity bonds and the reformulation of compositional rules in terms of hypergraph rewrites leads to a natural notion of a higher-arity category that demands novel mathematical theory.