Approximation properties of q-Araki-Woods algebras

Mateusz Wasilewski (IMPAN)

Tuesday 14th November, 2017 16:00-17:00 311B

Abstract

I will report on recent results about type III counterparts of q-Gaussian algebras -- the q-Araki-Woods algebras. In the first part of the talk I will survey known results about these algebras. Afterwards I will introduce the main tools: the Wick formula and the second quantisation. Then I will show how to use them to deduce the Haagerup property of q-Araki-Woods algebras. In the remainder of the talk I will focus on the complete metric approximation property; my plan is to briefly discuss the ultraproduct techniques, which are crucial for obtaining the result. This is joint work with Stephen Avsec and Michael Brannan.

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