Pythagorean representations of Thompson's groups
Arnaud Brothier, Vaughan F. R. Jones

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Homotopy and Cohomology in Algebraic Topology
