Projects per year
Organization profile
Organisation profile
The research team investigates mathematical structures that are important in several basic areas of mathematics like geometry, representation theory, functional analysis, differential calculus or theory of approximation. The motivation also comes from outside mathematics, from computer science or physics where some of the mathematical structures that are studied are called upon as models. By application of methods from category theory the relation between these mathematical structures is studied. The compatibility of their fundamental constructions is investigated and a general study of their representability, as well as of their function space theory is undertaken. More specifically the theory of frames or locales uses ordertheoretic notions to gain more insight in topological structures and to shed light on the use of choice principles in topology (or sometimes simply avoid them altogether). The theory of approach spaces provides the tools for obtaining quantified results in topology and in functional analysis, extending the isometric theory of Banach spaces. The team contributes to the development of the theory of semiabelian categories and tensor categories Semiabelian categories allow a unified setting for many important homological properties of nonabelian categories. Categories of quantum groups, of rings, of Liealgebras and of crossed modules are typical nonabelian categories, often with a tensor structure. Abstract tensor categories lead to interesting noncommutative spaces (operator algebras) whose analytical properties are studied in connection with the properties of the associated category. The main emphasis is on representation categories of quantum deformations of semisimple Lie groups.
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Profiles

Eva Colebunders
 Vrije Universiteit Brussel
 Vriendenkring VUB  Emeritus
 Topological Algebra, Functional Analysis and Category Theory
 Mathematics  Academic
Person: Sympathiser, Researcher, Professor

Kenny De Commer
 Vrije Universiteit Brussel
 Algebra and Analysis
 MathematicsTW  Academic
 Topological Algebra, Functional Analysis and Category Theory
 Mathematics  Academic
Person: Researcher, Professor

Tomas Everaert
 Vrije Universiteit Brussel
 MathematicsTW  Academic
 Algebra and Analysis
 Topological Algebra, Functional Analysis and Category Theory
 Mathematics  Academic
Person: Researcher, Guest professor

Mark Sioen
 Vrije Universiteit Brussel
 Algebra and Analysis
 Topological Algebra, Functional Analysis and Category Theory
 Mathematics  Academic
Person: Researcher, Professor

Gert Sonck
 Vrije Universiteit Brussel
 Algebra and Analysis
 Studiebegeleidingscentrum  Head of Department
 Mathematics  Head of Department, Academic
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor, Administrative/technical staff
Projects

OZR3284: Bilateral cooperation within the framework of a joint doctoral project: Bench Fee for Joint PhD VUBUAntwerpen, Van Den Haute Wouter
24/01/18 → 31/12/22
Project: Fundamental


CONI536: Inschrijvingen studenten (20152016 en 20162017) : Klaar voor de start
1/01/16 → 31/12/17
Project: Fundamental

CONI539: Inschrijvingen studenten (20152016 en 20162017): voorbereiding Chemie en Fysica
1/01/16 → 31/12/17
Project: Fundamental

CONI537: Ischrijvingen studenten (20152016 en 20162017): voorbereiding Wiskunde voor exacte wetenschappen
1/01/16 → 31/12/17
Project: Fundamental
Research output

Frames of continuous functions
Van Den Haute, W., Sioen, M. & Lowen, W., 15 Mar 2020, In : Topology and its Applications. 273, 106974.Research output: Contribution to journal › Article

Quantum flag manifolds, quantum symmetric spaces and their associated universal Kmatrices
De Commer, K. & Matassa, M., 3 Jun 2020, In : Advances in Mathematics. 366, p. 1100 100 p., 107029.Research output: Contribution to journal › Article

A characterisation of Lie algebras via algebraic exponentiation
GarcíaMartínez, X. & Van der Linden, T., 2019, In : Advances in Mathematics. 341, p. 92117 26 p.Research output: Contribution to journal › Article
6 Citations (Scopus) 
A Correspondence Between Homogeneous and Galois Coactions of Hopf Algebras
De Commer, K. & Konings, J., 1 May 2019, In : Algebras and Representation Theory. 23, 4, p. 13871416 30 p.Research output: Contribution to journal › Article

Actions of skew braces and settheoretic solutions of the reflection equation
De Commer, K., 2019, In : Proceedings of the Edinburgh Mathematical Society. 62, 4, p. 10891113 25 p.Research output: Contribution to journal › Article
4 Citations (Scopus)
Activities

Commissie Topsport VUB: Dual career at the Vrije Universiteit Brussel  New facts & figures
Koen De Brandt (Speaker), Paul Wylleman (Speaker), Evert Zinzen (Contributor), Gert Sonck (Contributor)14 Jan 2021Activity: Talk or presentation › Talk at a school event

A quantization of Sylvester's law of inertia
Kenny De Commer (Speaker)8 Oct 2020Activity: Talk or presentation › Talk or presentation at a workshop/seminar

A quantization of Sylvester's law of inertia
Kenny De Commer (Speaker)20 Nov 2020Activity: Talk or presentation › Talk or presentation at a workshop/seminar

Haonan Zhang
Kenny De Commer (Host)6 May 2019 → 10 May 2019Activity: Hosting a visitor › Hosting an academic visitor

Frederic Mynard
Mark Sioen (Host)31 Jan 2019 → 3 Feb 2019Activity: Hosting a visitor › Hosting an academic visitor