Phillips, JohnRaeburn, Iain2009-09-102009-09-1019932009-09-10http://hdl.handle.net/1828/1747We study the C*-algebras generated by projective isometric representations of semigroups using a dilation theorem and the structure theory of twisted crossed products. These algebras include the Toeplitz algebras of noncommutative tori recently studied by Ji, and similar algebras associated to the twisted group algebras of other groups such as the integer Heisenberg group.enTechnical Report