Monotone completions of the Fermion algebra

Let F be the Fermion C-*-algebra and let F-infinity be its (Pedersen) Borel (*)-envelope. Then there exists a sigma-ideal, M, the meagre ideal, such that F-infinity/M is the regular (sigma)-completion of F; a monotone complete type III factor which has no normal states. Also, there exists a sigma-ideal, N, such that F-infinity/N can be identified with the generic dynamics factor; a monotone complete type III factor which has no normal states. It might be considered plausible that M = N. We show here that this is false. There exists a central projection q in F-infinity such that q is in M and 1 - q is in N. Hence F-infinity = qM target (1 - q)N.