Page 183 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 183
OPERATOR ALGEBRAS (MS-14)
Elementary amenability and almost finiteness
David Kerr, kerrd@uni-muenster.de
University of Münster, Germany
We show that every free continuous action of a countably infinite elementary amenable group on
a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed
products of minimal such actions are Z-stable and classified by their Elliott invariant. This is
joint work with Petr Naryshkin.
A duality theorem for non-unital operator systems
Se Jin Kim, sejin.kim@glasgow.ac.uk
University of Glasgow, United Kingdom
Coauthors: Matthew Kennedy, Nicholas Manor
The recent work on nc convex sets of Davidson, Kennedy, and Shamovich show that there
is a rich interplay between the category of operator systems and the category of compact nc
convex sets, leading to new insights even in the case of C*-algebras. The category of nc convex
sets are a generalization of the usual notion of a compact convex set that provides meaningful
connections between convex theoretic notions and notions in operator system theory. In this
talk, we present a duality theorem for norm closed self-adjoint subspaces of B(H) that do not
necessarily contain the unit. We will present some insights this duality presents to various
notions in C*-algebras and operator systems such as simplicity. As well, we present a non-
commutative dynamical characterization of locally compact property (T) groups. This is joint
work with Matthew Kennedy and Nicholas Manor.
Positive trace polynomials
Igor Klep, igor.klep@fmf.uni-lj.si
University of Ljubljana, Slovenia
Trace polynomials are polynomials in noncommuting variables and traces of their products.
They can be naturally evaluated in finite von Neumann algebras. While originating in invari-
ant theory as equivariant maps between tuples of matrices, trace polynomials more recently
received attention in operator algebra, free probability and quantum information theory. This
talk addresses positivity of their evaluations and presents new Positivstellensätze (=algebraic
certificates for positivity) in terms of sums of squares and traces of sums of squares.
C*-algebras of right LCM monoids and their equilibrium states
Nadia Larsen, nadiasl@math.uio.no
University of Oslo, Norway
A right LCM monoid is characterised by the structural feature that the intersection of two princi-
pal right ideals is either empty or equal to another principal right ideal. The associated universal
181
Elementary amenability and almost finiteness
David Kerr, kerrd@uni-muenster.de
University of Münster, Germany
We show that every free continuous action of a countably infinite elementary amenable group on
a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed
products of minimal such actions are Z-stable and classified by their Elliott invariant. This is
joint work with Petr Naryshkin.
A duality theorem for non-unital operator systems
Se Jin Kim, sejin.kim@glasgow.ac.uk
University of Glasgow, United Kingdom
Coauthors: Matthew Kennedy, Nicholas Manor
The recent work on nc convex sets of Davidson, Kennedy, and Shamovich show that there
is a rich interplay between the category of operator systems and the category of compact nc
convex sets, leading to new insights even in the case of C*-algebras. The category of nc convex
sets are a generalization of the usual notion of a compact convex set that provides meaningful
connections between convex theoretic notions and notions in operator system theory. In this
talk, we present a duality theorem for norm closed self-adjoint subspaces of B(H) that do not
necessarily contain the unit. We will present some insights this duality presents to various
notions in C*-algebras and operator systems such as simplicity. As well, we present a non-
commutative dynamical characterization of locally compact property (T) groups. This is joint
work with Matthew Kennedy and Nicholas Manor.
Positive trace polynomials
Igor Klep, igor.klep@fmf.uni-lj.si
University of Ljubljana, Slovenia
Trace polynomials are polynomials in noncommuting variables and traces of their products.
They can be naturally evaluated in finite von Neumann algebras. While originating in invari-
ant theory as equivariant maps between tuples of matrices, trace polynomials more recently
received attention in operator algebra, free probability and quantum information theory. This
talk addresses positivity of their evaluations and presents new Positivstellensätze (=algebraic
certificates for positivity) in terms of sums of squares and traces of sums of squares.
C*-algebras of right LCM monoids and their equilibrium states
Nadia Larsen, nadiasl@math.uio.no
University of Oslo, Norway
A right LCM monoid is characterised by the structural feature that the intersection of two princi-
pal right ideals is either empty or equal to another principal right ideal. The associated universal
181
