Year: 2025
Type: preprint
Abstract: We study cocycle perturbations of state preserving actions on type $\mathrm{III}_1$ factors. Extending the theorem of Marrakchi and Vaes for type $\mathrm{II}_1$ factors, we show that a state preserving outer $\mathbb Z$-action on a type $\mathrm{III}_1$ factor with trivial bicentralizer admits a unitary cocycle whose perturbation becomes an ergodic action. This partially answers a question of Marrakchi and Vaes. A major difference from the type $\mathrm{II}$ case is that the modular automorphism group naturally appears as part of the action, making the construction of the required cocycle more delicate.
Source: arXiv (Cornell University)
Author: Isono, Yusuke
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 作用素環を用いた群作用の研究
OpenAlex ID: W4417452948
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