Liting properties for C*-algebras : Local versus Global

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• Gilles Pisier (Texas A&M University)
• Tuesday 09 April 2024, 11:30-12:30
• Seminar Room 1, Newton Institute.

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OOEW04 - Structure and Randomness - a celebration of the mathematics of Timothy Gowers

The main problem we will consider is whether for a C-algebra the local lifting property (LLP)  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 suspect that our recently constructed examples of  non-exact $C^$-algebras with both LLP and the weak expectation property (WEP) might lead to a counterexample to this local implies global problem. We will describe all the preceding properties from the tensor product viewpoint :  indeed LLP , LP, and WEP each admit a very simple characterization in terms of minimal and maximal tensor products.

This talk is part of the Isaac Newton Institute Seminar Series series.

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