Page 188 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
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OPERATOR ALGEBRAS (MS-14)
invariants.
Motivated by developing the general theory of quantum graphs, I will take a look at random
quantum graphs, having in mind that the study of random classical graphs is very fruitful. I will
show how having multiple perspectives on the notion of a quantum graph is useful in determin-
ing the symmetries of these objects – as expected, a generic quantum graph is asymmetric.
Stable rank one and Cuntz semigroup regularity
Wilhelm Winter, wwinter@uni-muenster.de
WWU Münster, Germany
A unital C*-algebra has stable rank one if its group of invertible elements is norm dense. While
this plays an important role for many structural results especially for simple C*-algebras, its
interplay with other regularity properties is subtle and somewhat mysterious.
Thiel has shown that if a simple unital C*-algebra has stable rank one and strict comparison
of positive elements, then its Cuntz semigroup is almost divisible.
In this talk I will describe a partial converse: strict comparison and almost divisibility to-
gether imply stable rank one.
This is joint work in progress with Shirly Geffen.
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invariants.
Motivated by developing the general theory of quantum graphs, I will take a look at random
quantum graphs, having in mind that the study of random classical graphs is very fruitful. I will
show how having multiple perspectives on the notion of a quantum graph is useful in determin-
ing the symmetries of these objects – as expected, a generic quantum graph is asymmetric.
Stable rank one and Cuntz semigroup regularity
Wilhelm Winter, wwinter@uni-muenster.de
WWU Münster, Germany
A unital C*-algebra has stable rank one if its group of invertible elements is norm dense. While
this plays an important role for many structural results especially for simple C*-algebras, its
interplay with other regularity properties is subtle and somewhat mysterious.
Thiel has shown that if a simple unital C*-algebra has stable rank one and strict comparison
of positive elements, then its Cuntz semigroup is almost divisible.
In this talk I will describe a partial converse: strict comparison and almost divisibility to-
gether imply stable rank one.
This is joint work in progress with Shirly Geffen.
186
