Research team
Expertise
Application related to non commutative space e.g. in economy, process evaluation etc.
Equivariant Brauer groups and Galois deformations 2.
Abstract
We study the Brauer group of some concrete monoidal categories, with emphasis on the equivariant Brauer group of a triangular pointed Hopf algebra, the Brauer group of differential graded algebras, and the Brauer group of a coquasitriangular dual pointed Hopf algebra. We will study the groupoid of biGalois objects over a Hopf algebra. We will introduce a categorical version of the Clifford functor and the Brauer-Wall group.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Structural theory of learning processes.
Abstract
The learning process as an aspect deformation of a causally ordered process on learning molecules.Researcher(s)
- Promoter: Van Oystaeyen Fred
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- Research Project
Mathematics, noncommutative algebra.
Abstract
Regularity and geometric structure of noncommutative algebras as function rings of noncommutative varieties.Researcher(s)
- Promoter: Van Oystaeyen Fred
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Project type(s)
- Research Project
Deformations and cohomology in non-commutative derived geometry.
Abstract
My research project is at the crossroads of non-commutative geometry (in the sense of Kontsevich, Van den Bergh, . . . ) and homotopical derived geometry (in the sense of Toën, . . . ). An important inspiration is the fact [6] that a smooth proper scheme is equivalent in the derived sense to a differential graded (dg) algebra [28], and smoothness and properness boil down to properties of this dg algebra. Hence, dg algebras become models of "noncommutative schemes" [37], [60]. This approach has proven useful in topics ranging from deformation quantization to homological mirror symmetry. In this spirit, we study dg algebras [28], their twins, A1-algebras [27], stacks, and in particular deformations and Hochschild cohomology of these objects.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Lowen Wendy
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- Research Project
Properties of crystalline graded rings with as base ring (degree 0) a Dedekind Domain.
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Neijens Tim
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- Research Project
FWO-Visiting Postdoctoral Fellowship. (Florin PANAITE, Romania)
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Panaite Florin
Research team(s)
Project type(s)
- Research Project
Modular forms in non-commutatieve geometry.
Abstract
During the previous years the candidate has studied Clifford algebra valued modular forms on arithmetic subgroups of the orthogonal group O(1,n) and that are annihilated by Dirac type operators. The aim of this project is to apply and to extend these techniques to generalizations of Clifford algebras. This shall give further insight in the study of discrete quantum groups and Hopf algebras in the framework of non-commutative geometry.Researcher(s)
- Promoter: Van Oystaeyen Fred
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- Research Project
Sheaves on a non-commutative topology: further development of the theory and its applications in algebra, geometry and logic.
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Stubbe Isar
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- Research Project
Deformation quantization methods for algebras and categories with applications to quantummechanics.
Projective Representations - Generalized Clifford Algebra - Dirac Formalism.
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Neijens Tim
Research team(s)
Project type(s)
- Research Project
New techniques in Hopf algebras and graded ring theory.
LIEGRITS - Flags, Quivers and Invariant Theory in Lie Representation Theory.
Construction and applications of non-communatieve geometry: from algebra to physics.
Hopf algebras in algebra, topology, geometry and physics.
European Priority Programme : 'Noncommutative Geometry'.
Abstract
Recent interactions between physics and noncommutative algebra gave rise to the creation of a new area in mathematics : 'Noncommutative Geometry'. The European Science Foundation selected this for a European Priority Programme that was funded by 12 member countries. The NOG-programme is involved in the organization of congresses, workshops and summerschools and also provides fellowships and travel grants for research cooperation. See web-page win-www.uia.ac.be/u/nog2000 for more information.Researcher(s)
- Promoter: Van Oystaeyen Fred
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- Research Project
Non commutative geometry and cohomology.
Abstract
Non commutative geometry, originally a part of abstract algebra nowadays is popular because of its applications in physics (quantum groups, Witten gauge algebras, ...), where different branches of the geometry are combined : differential geometry and C-algebras, quantum cohomology theories etc....Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Invariants and representation theory.
Abstract
Representations of Algebraic and Quantum Groups with Particular attention towards Lie algebras and Quantied Envelop Algebras. The team contains the reading Research Groups in this field.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Classificiation of simple modules over Weyl algebras.
Abstract
The project aims at the complete classification of Simple Modules over a class of recently very popular algebras. For higher WEYL- algebras and Rings of Differential Operators on Surfaces we aim to classify Holonomic Simple Modules.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Bavula Vladimir
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- Research Project
Mathematical methods of technology; motion planning for mobile robots.
Abstract
Motion planning for mobile robots is the part of the programme where a simulation-desktop software is developed and used for programming and calibrating mobile (welding-) robots.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Construction of a new part of the curriculum : mathematical methods of technology.
Abstract
Modern Pure Mathematics recently found new exciting applications in technology, particularly in connection with robotics (Motion Planning and Vision) or telecommunication(Coding). The Mathematical Theories necessary have been developed in a European Programme. Now these are furthered on an Educational level.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Noncommunative algebra and geometry with focus on representation theory.
Abstract
The representation theory of quantum groups and quantum spaces has several connections to non-communative geometry, e.g. determination of prime spectra, irrudicible representations, holonomic modules etc...Researcher(s)
- Promoter: Van Oystaeyen Fred
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- Research Project
Fundamental Mathematics.
Abstract
The library is, in all its aspects, the research lakoratory in mathematica. This is certainly the case for fundamental mathematica. With the promised money books will be purchased. As such the research in algebra end analysis/stochastics will be enhanced.Researcher(s)
- Promoter: Van Casteren Jan
- Co-promoter: Le Bruyn Lieven
- Co-promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Creation of a new curriculum in mathematical methods of technology.
Abstract
Pure mathematical techniques nowadays find new application in robotics (mobile robots, motion planning, vision) and Telecommunications (coding theory, encryptography...). New courses are being developed and tested.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Hopf algebras and co-galois theory.
Abstract
Study of actions and co-actions of Hopf Algebras, in particular Quantum Groups. Galois and co-Galois extensions with respect to Hopf Algebras are one of the main topics.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Scientific collaboration with the University of Bucarest on analytical chemistry, algebra and Romanian language.
Abstract
To start collaboration through the exchange of postdoctoral researchers within the specialisations mentioned in the title.Researcher(s)
- Promoter: Adams Freddy
- Co-promoter: Tasmowski Liliane
- Co-promoter: Van Oystaeyen Fred
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- Research Project
Brauer invariants in the representation theory of finite groups.
Abstract
Invariants connected to the Brauer group, usually of cohomological nature, appear in the representation theory of finite groups via projective representatitions and Schur multipliers.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Algebraic K-theory, groups and categories.
Abstract
New methods for studying higher K-groups and homology groups. Introducing K-theory of braided monoidal categories.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Hopf algebra and quantum group actions and coactions.
Abstract
Group actions and group gradings extend to Hopf algebra as well as quantum group actions and coactions. The structural properties of these objects may be studied in terms of invariants and semi-invariants.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
AMS-Benelux-meeting : Mathematics 2000.
Abstract
Treats topics at the forefront of actual scientific developments, redefining the position of mathematics in the world today. New applications of otherwise pure mathematics are investigated.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Invariants and representation theory of algebras and groups.
Abstract
Invariant theory, orbit methods and crystalization theory in connection with quantized envelopping algebras and quantum groups. Via Hall algebras a connection with the representation theory of finite dimensional algebras is created and studied.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Non commutative algebra and geometry with attention towards representation theory.
Abstract
Application of the non commutative geometry of the space Proj to the structure theory of algebras of quantum type. Representation theory of quantum groups and quasi-triangular Hopf algebras.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
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- Research Project
Quantized algebras: representations and weight modules.
Abstract
We study certain classes of quantized algebras and their representations in connection with their non-communative geometry. Specific classes of modules are treated in detail. We try to apply "braided techniques" to this theory.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Co-promoter: Le Bruyn Lieven
Research team(s)
Project type(s)
- Research Project
Quantum sections and gauge algebras for rings of differential operators over algebraic varieties.
Abstract
Iterated gauge algebras associated to rings of differential operators on projective varieties are schematic algebras, therefore it is possible to study their non-communative geometry by looking at their quantum sections.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Van Rompay Kristel
Research team(s)
Project type(s)
- Research Project
Analytical and algebraic methods for quantum fluctuations in the hydrodynamical limit.
Abstract
The methods of quantum-deformations applied to C-algebras have applications in physics. This project aims to build a bridge between quantumfluctuations appearing in the hydrodynamic limit and Hopf-algebraic methods in quantum group theory.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Rajczyk Elias
Research team(s)
Project type(s)
- Research Project
Enveloping algebras, quantum groups and representative theory.
Abstract
The noncommutative qeometry of quantum algebras including quantum enveloping algebras of Lie algebras or super color Lie algebras, gauge algebras and general schematic algebras, is being studied from a representation theoretic point of view.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Quantum sections of Micro-structure sheaves and Gauge-algebras for enveloping algebras of Lie Algebras
Abstract
The graded Rees rings of filtrations having a quantum-space for the associated graded ring may be viewed as objects over a non-commutative projective space. We aim to study the arithmetical properties of these objectsResearcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Willaert Luc
Research team(s)
Project type(s)
- Research Project
Quantum sections and gauge algebras for rings of differential operators over algebraic varieties.
Abstract
Iterated gauge algebras associated to rings of differential operators on projective varieties are schematic algebras, therefore it is possible to study their non-communative geometry by looking at their quantum sections.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Van Rompay Kristel
Research team(s)
Project type(s)
- Research Project
Analytical and algebraic methods for quantum fluctuations in the hydrodynamical limit.
Abstract
The methods of quantum-deformations applied to C-algebras have applications in physics. This project aims to build a bridge between quantumfluctuations appearing in the hydrodynamic limit and Hopf-algebraic methods in quantum group theory.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Rajczyk Elias
Research team(s)
Project type(s)
- Research Project
K-theoretic approach to the Brauer group and quadratic forms.
Abstract
Mercuriev-Suslin 's theorem relates the K-group K2 of a field to the cohomology H2, hence to the Brauer group. The 2-torsion part is connected to certain quadratic forms over the ground field.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Structure of finite dimensional algebras and their representations.
Abstract
The structure of finite dimensional associative algebras and Lie algebras is being investigated.Researcher(s)
- Promoter: Van Oystaeyen Fred
Research team(s)
Project type(s)
- Research Project
Quantum sections of Micro-structure sheaves and Gauge-algebras for enveloping algebras of Lie Algebras
Abstract
The graded Rees rings of filtrations having a quantum-space for the associated graded ring may be viewed as objects over a non-commutative projective space. We aim to study the arithmetical properties of these objectsResearcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Willaert Luc
Research team(s)
Project type(s)
- Research Project
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Van Rompay Kristel
Research team(s)
Project type(s)
- Research Project
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Molenberghs Geert
Research team(s)
Project type(s)
- Research Project
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Van den Bergh Michel
Research team(s)
Project type(s)
- Research Project
Hopf algebra actions and the ring of invariants or semi-invariants related to quantum spaces and quantum groups.
Abstract
Hopf algebra actions on algebra extensions may be viewed as an extension of classical Galois theory. Induction and coinduction from invariants is being studied.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Co-promoter: Le Bruyn Lieven
Research team(s)
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- Research Project
Abstract
Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Van den Bergh Michel
Research team(s)
Project type(s)
- Research Project
Geometry of matrixinvariants and arithmetic geometry.
Abstract
Rationality problem for quotients of PFLn-varieties. Connection between ringtheoretical properties of Sklyanin algebras and arithmetic of elliptic curves.Researcher(s)
- Promoter: Van Oystaeyen Fred
- Fellow: Le Bruyn Lieven
Research team(s)
Project type(s)
- Research Project