CROSSED PRODUCT DECOMPOSITIONS OF A PURELY INFINITE VON-NEUMANN ALGEBRA WITH FAITHFUL, ALMOST-PERIODIC WEIGHT

For M a separable, purely infinite von Neumann algebra with almost per iodic weight phi, Connes' decomposition of M as a crossed product of a semifinite von Neumann algebra by a trace-scaling action of a countab le abelian group is described, and factoriality is related to ergodici ty of a certain partial action. Then Takasaki's continuous decompositi on of the same algebra is related to the above discrete decomposition via Takesaki's notion of induced action, but here one induces up from a dense subgroup. The above results are used to give a model for the o ne-parameter trace-scaling action of R(+) on the injective IIinfinity factor. Finally, another model of the same action, due to work of Aub ert and explained by Jones, is described.