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University of Sydney Algebra Seminar

Arnaud Brothier

Friday 1 September, 12-1pm, Place: Carslaw 173

Classification of representations of the Richard Thompson groups and of the Cuntz algebra

Vaughan Jones technology permits to lift functors to group actions of fraction groups. This provides new ways to build explicit unitary representations of the Richard Thompson groups F,T,V. I will introduce the so-called Pythagorean C*-algebra and explain how representation of it yield representations of the three Thompson groups and additionally of the Cuntz algebra. I will then explain how to reduce difficult problems concerning irreducibility and unitarily conjugacy of those representations into finite dimensional linear algebra and how beautiful moduli spaces naturally emerge. This is a joint work with Dilshan Wijesena that continues a previous collaboration with Vaughan Jones.