Arbre de Noël du GDR "Géométrie non-commutative"

Propriétés de relèvement pour les C∗-algèbres : du local au global ?

1 déc. 2022, 09:30

1h

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Orateur

Prof. Gilles PISIER (Sorbonne Université - Texas A&M University)

Description

The main problem we will consider is whether the local lifting property (LLP) of a $C^{\ast }$-algebra implies the (global) lifting property (LP). Kirchberg showed that this holds if the Connes embedding problem has a positive solution, but it might hold even if its solution is negative. We will present several new characterizations of the lifting property for a $C^{\ast }$-algebra $A$ in terms of the maximal tensor product of A with the (full) $C^{\ast }$-algebra of the free group ${\mathbb{F}}_{\mathrm{\infty }}$. We will recall our recent construction of a non-exact $C^{\ast }$-algebra with both LLP and WEP. This prompted us to try to prove that LLP implies LP for a WEP $C^{\ast }$-algebra. While our investigation is not conclusive we obtain a fairly simple condition in terms of tensor products that is equivalent to the validity of the latter implication.

Documents de présentation

Vidéo