q-COMMUTING DILATION.

In this paper, we prove that any pair of q-commuting contractions on a Hilbert space dilates to a pair of q-commuting unitaries, where |q| = 1. We generalize this result to a (G, q)-commuting n-tuple (T1, . . . , Tn) of strict contractions, where G is an acyclic graph with vertex set {1, . . . ,n}. We further generalize it to a family of (G, q)-commuting strict contractions, where G is an acyclic graph on an infinite set of vertices. [ABSTRACT FROM AUTHOR]