Non-uniqueness of continuous trace-scaling flows on certain full factors
We show that if M is a full II_infinity factor such that the fundamental group of a finite corner is R and Out(M) is a locally compact second countable group, then M admits either a unique continuous trace scaling flow or a continuum of pairwise distinct ones, up to cocycle conjugacy. Equivalently, there is either a unique III_1 factor or a continuum of pairwise non-isomorphic III_1 factors with continuous core M. We apply this dichotomy result to factors constructed in [Dep12] and [Cha25] where Out(M) is a Lie group. We also give two independent constructions of full factors admitting a continuum of pairwise distinct trace-scaling flows where the outer automorphism group is unknown.
math.OA↗