Page 187 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 187
OPERATOR ALGEBRAS (MS-14)
intertwinings, the talk will focus on how to exploit equivariant Kasparov theory for the purpose
of classification. This leads to a strengthening of the Cuntz-Thomsen picture of equivariant
KK-theory in the spirit of Lin and Dadarlat-Eilers, which is the main result of the talk. If time
permits, I will speculate on some far-reaching consequences of this machinery. This is joint
work with James Gabe.
Order isomorphisms of operator intervals
Peter Šemrl, peter.semrl@fmf.uni-lj.si
University of Ljubljana, Slovenia
A general theory of order isomorphisms of operator intervals will be presented. It unifies
and extends several known results, among others Ludwig’s description of ortho-order auto-
morphisms of effect algebras and Molnar’s characterization of bijective order preserving maps
on bounded observables. The problem of the existence and uniqueness of extensions of order
isomorphisms of operator intervals to operator domains will be discussed.
Higher structures in mathematics: buildings, C*-algebras and
Drinfeld-Manin solutions of Yang-Baxter equations
Alina Vdovina, alina.vdovina@ncl.ac.uk
Newcastle University, United Kingdom
The most interesting mathematical structures are usually sufficiently rich and appear in several
fields of mathematics, physics and computer science. We give a brief introduction to one such
topic, namely buildings. We will present geometric, algebraic and arithmetic aspects of build-
ings. In particular, we present explicit constructions of infinite families of quaternionic cube
complexes, covered by buildings.
We will use these cube complexes to describe new infinite families of Drinfeld-Manin so-
lutions of Yang-Baxter equations. Another application of our constructions are new infinite
families of higher-rank graph C*-algebras and von Neumann algebras.
Random quantum graphs are asymmetric
Mateusz Wasilewski, mateusz.wasilewski@kuleuven.be
KU Leuven, Belgium
Coauthor: Alexandru Chirvasitu
The study of quantum graphs emerged from quantum information theory. One way to define
them is to replace the space of functions on a vertex set of a classical graph with a noncommu-
tative algebra and find a satisfactory counterpart of an adjacency matrix in this context. Another
approach is to view undirected graphs as symmetric, reflexive relations and “quantize” the no-
tion of a relation on a set. In this case quantum graphs are operator systems and the definitions
are equivalent. Doing this has some consequences already for classical graphs; viewing them as
operator systems of a special type has already led to the introduction of a few new “quantum”
185
intertwinings, the talk will focus on how to exploit equivariant Kasparov theory for the purpose
of classification. This leads to a strengthening of the Cuntz-Thomsen picture of equivariant
KK-theory in the spirit of Lin and Dadarlat-Eilers, which is the main result of the talk. If time
permits, I will speculate on some far-reaching consequences of this machinery. This is joint
work with James Gabe.
Order isomorphisms of operator intervals
Peter Šemrl, peter.semrl@fmf.uni-lj.si
University of Ljubljana, Slovenia
A general theory of order isomorphisms of operator intervals will be presented. It unifies
and extends several known results, among others Ludwig’s description of ortho-order auto-
morphisms of effect algebras and Molnar’s characterization of bijective order preserving maps
on bounded observables. The problem of the existence and uniqueness of extensions of order
isomorphisms of operator intervals to operator domains will be discussed.
Higher structures in mathematics: buildings, C*-algebras and
Drinfeld-Manin solutions of Yang-Baxter equations
Alina Vdovina, alina.vdovina@ncl.ac.uk
Newcastle University, United Kingdom
The most interesting mathematical structures are usually sufficiently rich and appear in several
fields of mathematics, physics and computer science. We give a brief introduction to one such
topic, namely buildings. We will present geometric, algebraic and arithmetic aspects of build-
ings. In particular, we present explicit constructions of infinite families of quaternionic cube
complexes, covered by buildings.
We will use these cube complexes to describe new infinite families of Drinfeld-Manin so-
lutions of Yang-Baxter equations. Another application of our constructions are new infinite
families of higher-rank graph C*-algebras and von Neumann algebras.
Random quantum graphs are asymmetric
Mateusz Wasilewski, mateusz.wasilewski@kuleuven.be
KU Leuven, Belgium
Coauthor: Alexandru Chirvasitu
The study of quantum graphs emerged from quantum information theory. One way to define
them is to replace the space of functions on a vertex set of a classical graph with a noncommu-
tative algebra and find a satisfactory counterpart of an adjacency matrix in this context. Another
approach is to view undirected graphs as symmetric, reflexive relations and “quantize” the no-
tion of a relation on a set. In this case quantum graphs are operator systems and the definitions
are equivalent. Doing this has some consequences already for classical graphs; viewing them as
operator systems of a special type has already led to the introduction of a few new “quantum”
185
