Page 186 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 186
OPERATOR ALGEBRAS (MS-14)
C*-analog of an irreducible inclusion of von Neumann algebras (i.e., one with trivial relative
commutant). I will present an intrinsic description of when an inclusion of C*-algebras is C*-
irreducible, and relate this to the parallel situation of von Neumann algebras. I will further show
how C*-irreducible inclusions can arise from groups, dynamical systems, inductive limits (and
AF-algebras), and tensor products.
Quantum symmetry vs nonlocal symmetry
Simon Schmidt, Simon.Schmidt@glasgow.ac.uk
University of Glasgow, United Kingdom
We will introduce the notion of nonlocal symmetry of a graph G, defined as winning quantum
correlation for the G-automorphism game that cannot be produced classically. We investigate
the differences and similarities between this and the quantum symmetry of the graph G, defined
as non-commutativity of the algebra of functions on the quantum automorphism group of G.
We show that quantum symmetry is a necessary but not sufficient condition for nonlocal sym-
metry. In particular, we show that the complete graph on four points does not exhibit nonlocal
symmetry. We will also see that the complete graph on five or more points does have nonlocal
symmetry. This talk is based on joint work with David Roberson.
Constructions in minimal dynamics and applications to the classification
of C∗-algebras
Karen Strung, krstrung@gmail.com
Instiute of Mathematics of the Czech Academy of Sciences, Czech Republic
Coauthors: Robin Deeley, Ian Putnam
What abelian groups can arise as the K-theory of C∗-algebras arising from minimal dynamical
systems? In joint work with Robin Deeley and Ian Putnam, we completely characterize the
K-theory of the crossed product of a space X with finitely generated K-theory by an action of
the integers and show that crossed products by a minimal homeomorphisms exhaust the range
of these possible K-theories. We also investigate the K-theory and the Elliott invariants of
orbit-breaking algebras. We show that given arbitrary countable abelian groups G0 and G1 and
any Choquet simplex ∆ with finitely many extreme points, we can find a minimal orbit-breaking
relation such that the associated C∗-algebra has K-theory given by this pair of groups and tracial
state space affinely homeomorphic to ∆. These results have important applications to the Elliott
classification program for C∗-algebras. In particular, we make a step towards determining the
range of the Elliott invariant of the C∗-algebras associated to étale equivalence relations.
The stable uniqueness theorem for equivariant Kasparov theory
Gabor Szabo, gabor.szabo@kuleuven.be
KU Leuven, Belgium
In this talk I will present a new approach to the classification of C*-dynamics up to cocycle
conjugacy. After a few categorical preliminaries and a brief introduction to equivariant Elliott
184
C*-analog of an irreducible inclusion of von Neumann algebras (i.e., one with trivial relative
commutant). I will present an intrinsic description of when an inclusion of C*-algebras is C*-
irreducible, and relate this to the parallel situation of von Neumann algebras. I will further show
how C*-irreducible inclusions can arise from groups, dynamical systems, inductive limits (and
AF-algebras), and tensor products.
Quantum symmetry vs nonlocal symmetry
Simon Schmidt, Simon.Schmidt@glasgow.ac.uk
University of Glasgow, United Kingdom
We will introduce the notion of nonlocal symmetry of a graph G, defined as winning quantum
correlation for the G-automorphism game that cannot be produced classically. We investigate
the differences and similarities between this and the quantum symmetry of the graph G, defined
as non-commutativity of the algebra of functions on the quantum automorphism group of G.
We show that quantum symmetry is a necessary but not sufficient condition for nonlocal sym-
metry. In particular, we show that the complete graph on four points does not exhibit nonlocal
symmetry. We will also see that the complete graph on five or more points does have nonlocal
symmetry. This talk is based on joint work with David Roberson.
Constructions in minimal dynamics and applications to the classification
of C∗-algebras
Karen Strung, krstrung@gmail.com
Instiute of Mathematics of the Czech Academy of Sciences, Czech Republic
Coauthors: Robin Deeley, Ian Putnam
What abelian groups can arise as the K-theory of C∗-algebras arising from minimal dynamical
systems? In joint work with Robin Deeley and Ian Putnam, we completely characterize the
K-theory of the crossed product of a space X with finitely generated K-theory by an action of
the integers and show that crossed products by a minimal homeomorphisms exhaust the range
of these possible K-theories. We also investigate the K-theory and the Elliott invariants of
orbit-breaking algebras. We show that given arbitrary countable abelian groups G0 and G1 and
any Choquet simplex ∆ with finitely many extreme points, we can find a minimal orbit-breaking
relation such that the associated C∗-algebra has K-theory given by this pair of groups and tracial
state space affinely homeomorphic to ∆. These results have important applications to the Elliott
classification program for C∗-algebras. In particular, we make a step towards determining the
range of the Elliott invariant of the C∗-algebras associated to étale equivalence relations.
The stable uniqueness theorem for equivariant Kasparov theory
Gabor Szabo, gabor.szabo@kuleuven.be
KU Leuven, Belgium
In this talk I will present a new approach to the classification of C*-dynamics up to cocycle
conjugacy. After a few categorical preliminaries and a brief introduction to equivariant Elliott
184
