Pythagorean representations of Thompson's groups

TL;DR

This paper introduces Pythagorean C*-algebras and develops a method to construct unitary representations of Thompson's groups using category and functor techniques, with several examples computed.

Contribution

It presents a novel approach to building Thompson group representations via Pythagorean C*-algebras and categorical methods, expanding the toolkit for studying these groups.

Findings

Constructed new unitary representations of Thompson's groups.

Defined Pythagorean C*-algebras and demonstrated their use.

Provided explicit examples of the representations.

Abstract

We introduce the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson's groups from representations of them. We calculate several examples.