Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples

Abstract

Let $G$ be a <i>finite group</i>. Consider the algebra $A$ of all complex functions on $G$ (with pointwise product). Define a coproduct $\Delta$ on $A$ by $\Delta(f)(p,q)=f(pq)$ where $f\in A$ and $p,q\in G$. Then $(A,\Delta)$ is a Hopf algebra. If