AI 中文总结
该研究针对特定全II_∞因子，证明其连续迹标度流在余圈共轭下的非唯一性二分结果，并应用于已知外自同构群的因子，还构造了外自同构群未知的此类因子。
AI 中文摘要
我们证明：若M是一个有限角基本群为R、外自同构群Out(M)为局部紧第二可数群的全II_∞因子，则M在余圈共轭下要么仅容许唯一的连续迹标度流，要么容许连续统个两两不同的此类流。等价地，存在唯一的III_1因子，或存在连续统个两两非同构且以M为连续核心的III_1因子。我们将此二分结果应用于[Dep12]和[Cha25]中构造的、Out(M)为李群的因子；还独立给出两类全因子的构造，这些因子容许连续统个两两不同的迹标度流，且其外自同构群未知。
英文摘要
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.
Commentsv1; 34 pages, comments welcome!
