AG Mathematische Physik, Fernando Lledó (Madrid): Examples of finite dimensional approximations in C*-algebras

Fernando Lledó (Madrid)

Examples of finite dimensional approximations in C*-algebras

Abstract:

Motivated by the shocking Banach-Tarski paradox and, in particular, by

Foelner type approximations of amenable groups, I will present finite

dimensional matrix approximations in two classes of operator algebras:

– The resolvent algebra introduced by Buchholz and Grundling in 2008 to

give an alternative bounded operator approach to the canonical commutation

relations (CCR) in quantum mechanics.

– The uniform Roe algebras of an inverse semigroup, where the inverse

semigroup is viewed as a metric space.

In this talk I will emphasize the importance of examples.

The results presented are included in the recent publications

[1] F. Lledó and D. Martínez, *A note on commutation relations and finite

dimensional approximations,* Expositiones Mathematicae *40* (2022) 947–960.

[2] F. Lledó and D. Martínez, *The uniform Roe algebra of an inverse

semigroup*, Journal of Mathematical Analysis and Applications *499 *(2021)

124996.

[3] P.Ara, F. Lledó and D. Martínez, Amenability and paradoxicality in

semigroups and C*-algebras, J. Funct. Anal. *279* (2020) 108530