Presentations of projective quantum groups (Q2673869)

This article is concerned with finding presentations of projective versions of compact matrix quantum groups. Given an orthogonal compact matrix quantum group \(G\) and a generating set for its representation category, the author constructs explicitly a generating set for the representation category of the projective version \(PG\) of \(G\). Via Woronowicz-Tannaka-Krein duality [\textit{S. L. Woronowicz}, Invent. Math. 93, No. 1, 35--76 (1988; Zbl 0664.58044)], one can then determine a presentation for \(PG\). As an application, it is proven that the projective versions of free unitary quantum groups and free orthogonal quantum groups coincide.