Work

Atomic representations of R. Thompson’s groups and Cuntz’s algebra

Year: 2025

Type: article

Abstract: We continue to study Pythagorean unitary representations of Richard Thompson’s groups F,T,V and their extension to the Cuntz(–Dixmier) algebra \mathcal{O} . Any linear isometry from a Hilbert space to its direct sum square produces such. We focus on those arising from a finite-dimensional Hilbert space. We show that they decompose as a direct sum of a so-called diffuse part and an atomic part. We previously proved that the diffuse part is Ind-mixing: it does not contain induced representations of finite-dimensional ones. In this article, we fully describe the atomic part it is a finite direct sum of irreducible monomial representations arising from a precise family of parabolic subgroups.

Source: Documenta Mathematica

DOI: 10.4171/dm/1031

Authors: Arnaud Brothier, Dilshan Wijesena

Institutions: University of Trieste, UNSW Sydney

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Australian Government, Australian Research Council

Award: Physical realisation of enriched quantum symmetries