Strong singularity for subalgebras of finite factors

TL;DR

This paper develops criteria for identifying strongly singular subalgebras within finite factors, especially those from group actions on geometric objects, advancing the understanding of their structure.

Contribution

It introduces new criteria for strong singularity and constructs examples of strongly singular subalgebras in type II_1 factors from geometric group actions.

Findings

Criteria for strong singularity in von Neumann subalgebras

Construction of strongly singular subalgebras from geometric group actions

Identification of geometric conditions leading to strong singularity

Abstract

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular subalgebras. We particularly focus on groups which act on geometric objects, where the underlying geometry leads to strong singularity.