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 order-theoretic 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 semi-abelian categories and tensor categories Semi-abelian categories allow a unified setting for many important homological properties of non-abelian categories. Categories of quantum groups, of rings, of Lie-algebras and of crossed modules are typical non-abelian categories, often with a tensor structure. Abstract tensor categories lead to interesting non-commutative 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 semi-simple Lie groups.
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Network
Profiles
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Eva Colebunders
- Vrije Universiteit Brussel
- Vriendenkring VUB - Emeritus
- Topological Algebra, Functional Analysis and Category Theory
- Mathematics - Academic
Person: Sympathiser, Researcher, Professor
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Kenny De Commer
- Vrije Universiteit Brussel
- Algebra and Analysis
- Mathematics-TW - Academic
- Topological Algebra, Functional Analysis and Category Theory
- Mathematics - Academic
Person: Researcher, Professor
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Tomas Everaert
- Vrije Universiteit Brussel
- Mathematics-TW - Academic
- Algebra and Analysis
- Topological Algebra, Functional Analysis and Category Theory
- Mathematics - Academic
Person: Researcher, Guest professor
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Mark Sioen
- Vrije Universiteit Brussel
- Algebra and Analysis
- Topological Algebra, Functional Analysis and Category Theory
- Mathematics - Academic
Person: Researcher, Professor
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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
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OZR3284: Bilateral cooperation within the framework of a joint doctoral project: Bench Fee for Joint PhD VUB-UAntwerpen, Van Den Haute Wouter
24/01/18 → 31/12/22
Project: Fundamental
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CONI536: Inschrijvingen studenten (2015-2016 en 2016-2017) : Klaar voor de start
1/01/16 → 31/12/17
Project: Fundamental
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CONI539: Inschrijvingen studenten (2015-2016 en 2016-2017): voorbereiding Chemie en Fysica
1/01/16 → 31/12/17
Project: Fundamental
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CONI537: Ischrijvingen studenten (2015-2016 en 2016-2017): voorbereiding Wiskunde voor exacte wetenschappen
1/01/16 → 31/12/17
Project: Fundamental
Research output
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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
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Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
De Commer, K. & Matassa, M., 3 Jun 2020, In : Advances in Mathematics. 366, p. 1-100 100 p., 107029.Research output: Contribution to journal › Article
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A characterisation of Lie algebras via algebraic exponentiation
García-Martínez, X. & Van der Linden, T., 2019, In : Advances in Mathematics. 341, p. 92-117 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. 1387-1416 30 p.Research output: Contribution to journal › Article
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Actions of skew braces and set-theoretic solutions of the reflection equation
De Commer, K., 2019, In : Proceedings of the Edinburgh Mathematical Society. 62, 4, p. 1089-1113 25 p.Research output: Contribution to journal › Article
4 Citations (Scopus)
Activities
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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
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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
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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
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Haonan Zhang
Kenny De Commer (Host)6 May 2019 → 10 May 2019Activity: Hosting a visitor › Hosting an academic visitor
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Frederic Mynard
Mark Sioen (Host)31 Jan 2019 → 3 Feb 2019Activity: Hosting a visitor › Hosting an academic visitor