Effective subfactor theory

TL;DR

This paper characterizes when a subfactor is oracle computable based on the computability of key structures like the Jones basic construction and conditional expectations, with illustrative examples.

Contribution

It introduces a new characterization of subfactor computability using Jones basic construction and Pimsner-Popa bases.

Findings

Subfactor oracle computability is characterized by the computability of the Jones basic construction.

Computability of the conditional expectation map is equivalent to subfactor computability.

Examples demonstrate the applicability of the main theorem.

Abstract

We characterize when a subfactor $N\subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction, in terms of computable Pismner-Popa bases, and in terms of computability of the conditional expectation map. We illustrate our main theorem with some examples.