Woronowicz Tannaka-Krein duality and free orthogonal quantum groups

Abstract

Given a finite-dimensional Hilbert space H and a collection of operators between its tensor powers satisfying certain properties, we give a short proof of the existence of a compact quantum group G with a fundamental representation U on H such that the intertwiners between the tensor powers of U coincide with the given collection of operators. We then explain how the general version of Woronowicz Tannaka-Krein duality can be deduced from this. © 2017 Mathematica Scandinavica