IRIOA · Interactions between reversible and irreversible Operator Algebras.
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2019-09-05 → 2021-12-23
- EU contribution
- €207,312
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Interactions between reversible and irreversible Operator Algebras.
We proposed a systematic study of interactions between self-adjoint (reversible) and non-self-adjoint (irreversible) operator algebras. The goals of this proposal were as follows: Goal A was to advance the structure theory of semigroup C*-algebras and boundary quotient C*-algebras. Goal B was to extend work of the ER with Katsoulis to the non-abelian group-graded context and determine the C*-envelope of the irreversible tensor algebras. Goal C was to obtain new classification results for reversible and irreversible operator algebras. he issues that were addressed regarding Goal A and Goal B had to do with the required development of new coaction quantum symmetry methods, in order to solve problems on residual finite dimensionality and co-universality of irreversible operator algebras. Another issue that has to do with Goal C was to find precise connections between classification problems of irreversible and reversible operator algebras. The results obtained for this project were original and innovative, and have impacted the field. Each project led to significant transfer of knowledge between the ER and the supervisor as well as the group in operator algebras at Copenhagen University. This MSC IF has influence on the ER's career and enabled him to obtain a permanent academic position at Haifa University in Israel. On top of all this, the ER has significantly broadened his research network in Europe, and has collaborated with internationally recognized European experts in operator algebras. These include Soren Eilers, Xin Li, Evgenios Kakariadis and Toke Carlsen. The ER has obtained new expertise in classification of C*-algebras, which has diversified his research profile in new directions of interest to experts in Europe. The ERs organizational skills have improved after organizing a conference, and he will continue to organize meetings on the topics of the proposal in 2022. The ERs supervision skills have improved after successfully co-supervising a Masters student and taking the course on supervision of MSc and BSc students. The ERs outreach activities have become more prominent with at least one outreach lecture each year, with many more to come as the ER plans to deliver outreach talks to highschool students in the north of Israel.
Data: CORDIS, © European Union
Project objective
We propose a systematic study of interactions between self-adjoint (reversible) and non-self-adjoint (irreversible) operator algebras. We shall import Arveson's C*-envelope and Hamana's non-commutative Furstenberg boundary to the group-graded contexts, and use them to obtain new structural, dilation and classification results for various operator algebras. The goals of this proposal are as follows: Goal A is to advance the structure theory of semigroup Nica C*-algebras and Crisp-Laca boundary quotient C*-algebras, with applications in semigroup theory. This will be achieved by adapting Hamana boundary techniques used in a recent breakthrough characterization of simplicity of reduced group C*-algebras due to Kennedy and Kalantar. Goal B is to extend work of the ER with Katsoulis to the non-abelian group-graded context and determine if the C*-envelope of the irreversible tensor algebras in Fowler's context is the Cuntz-Nica-Pimsner algebra. Applications include new Laca-type dilation results, Hao-Ng isomorphisms and non-commutative Takai-type duality. Goal C is to obtain new classification results for reversible and irreversible operator algebras by a two-way flow between the theories. This will be done by uncovering the hierarchy between invariants of C*-algebras with additional structure and of non-self-adjoint operator algebras, leading to insight on an open problem of Davidson and Katsoulis in dynamics. The anticipated results in the proposal are original and innovative, and will have an impact on the field well after the end of the fellowship. Each project is chosen to optimize the transfer of knowledge between the ER and the supervisor as well as the group in operator algebras at Copenhagen University. Considering the ambitious research program, supervision, outreach, as well as other activities suggested, the MSC IF will have a lasting influence on the ER's career and will allow him to obtain a permanent academic position after the completion of the fellowship.
Original text from CORDIS.
Participants
- KOBENHAVNS UNIVERSITET · KOBENHAVNCoordinatorDenmark
Links
Data: CORDIS, © European Union