Fernando Lledó (Universidad Carlos III Madrid): Amenability and paradoxical decompositions around Roe C*-algebras. Oberseminar C*-Algebren
Tuesday, 10.05.2016 16:00 im Raum M6
Abstract:
"There is a classical mathematical theorem (based on the work by Banach and Tarski) that implies the following shocking statement: An orange
can be divided into finitely many pieces, these pieces can be moved and
rearranged in such a way to yield two oranges of the same size as the original
one. In 1929 J. von Neumann recognized that one of the reasons underlying
the Banach-Tarski paradox is the fact that on the unit ball there
is an action of a discrete subgroup of isometries that fails to have the property
of amenability ("Mittelbarkeit in German).
In this talk we will approach the concept of amenability and paradoxcial
decompositions from very different perspectives:
we will analyze metric, purely algebraic and operator
algebraic aspects. In particular, we will define the class of Foelner C*-algebras
in terms of a net of unital completely positive maps from the algebra to matrices
that are asymptotically multiplicative in a weak sense.
This class of C*-algebras include the quasidiagonal ones.
Finally, we will present Roe C*-algebras associated to discrete
metric spaces with bounded geometry as an example where all these
approaches unify.
(Joint work with P Ara (UAB), K. Li and J. Wu (U. Münster))."
Angelegt am 30.03.2016 von Elke Enning
Geändert am 20.04.2016 von Elke Enning
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