Objective
"This project will investigate the structure and representation theory of quantized enveloping algebras of finite dimensional semisimple complex Lie algebras and of affine Kac-Moody algebras, and of other algebras closely related to them: Hall algebras and (quantized) Schur algebras. The project's starting point is a construction, due to Beilinson, Lusztig and MacPherson, of an epimorphism from a type A quantum group onto a Schur algebra. So far, this construction has been limited to type A (with linear orientation on the positive part). The project aims at extending this result to general Dynkin or even affine (extended Dynkin) type. The project will take the following novel approach. At the beginning, it will restrict to the positive parts of quantized en veloping algebras. These can be identified with Hall (affine type: composition) algebras of quivers. Then representation theory (Auslander Reiten theory and covering theory) and geometry of quivers will be used to define and construct positive Schur algebr as quotients and to describe the kernels of these epimorphisms. Using representation theory of finite dimensional algebras and homological algebra, the structure of positive Schur will then be described. Using Drinfeld double constructions and derived c ategories (especially root categories), the information obtained will then be transferred from positive to full Schur algebras and to quantum groups. Quantum groups and Schur algebras have a wide range of applications, ranging from Lie algebras and algebr aic groups or symmetric groups and finite groups of Lie type over knot theory, homotopy theory, K-theory and functor cohomology to mathematical physics and quantum field theory. The project will extend a fundamental technique in this area and it is designed to be part of a long-term and large-scale project, with a range of abstract and computational applications."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics topology knot theory
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics topology algebraic topology
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-7
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
IIF - Marie Curie actions-Incoming International Fellowships
Coordinator
KOELN
Germany
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.