On coherent Hopf 2-algebras

TL;DR

This paper constructs a new class of algebraic structures called coherent Hopf 2-algebras using Hopf coquasigroups, relaxing coassociativity and exploring their properties and examples.

Contribution

It introduces coherent Hopf 2-algebras based on Hopf coquasigroups and studies their quasi coassociative variants with explicit examples.

Findings

Relaxed coassociativity in Hopf coquasigroups leads to coherent Hopf 2-algebras.

Quasi coassociative Hopf coquasigroups produce coherent Hopf 2-algebras with nontrivial coassociators.

The algebra of functions on a Cayley algebra basis exemplifies these structures.

Abstract

We construct a coherent Hopf 2-algebra in terms of Hopf coquasigroups, which relax the coassociativity condition and generalize the results in \cite{XH2023}. We also study quasi coassociative Hopf coquasigroups, and show that they give rise to coherent Hopf 2-algebras with nontrivial coassociators. As an example, we investigate the algebra of functions on a Cayley algebra basis.