Compact quantum group

Summary

A compact quantum group is a unital C*-algebra with a coassociative comultiplication that satisfies a cancellation condition. It was introduced by Stanisław Woronowicz as the noncommutative analogue of a compact group, seen through its algebra of continuous functions. Every compact group gives one, and there are genuinely quantum examples such as $SU_q(2)$. Much of the theory of compact groups survives: there is a unique Haar state, and finite-dimensional representations behave as in Peter–Weyl theory.