Orthogonal decompositions and twisted isometries

Let [Formula: see text]. text] be commuting unitaries on some Hilbert space text], and suppose An text]-tuple of isometries is called text]-twisted isometry with respect to (or simply if clear from the context) text]’s are in commutator We prove that each admits a von Neumann–Wold type orthogonal decomposition, universal text]-algebra generated by nuclear. exhibit concrete analytic models isometries, establish connections between unitary equivalence classes irreducible representations text]-algebras nonzero twisted noncommutative tori. Our motivation stems classical rotation Heisenberg group text]-algebras.