Objective
The subject of Quantum Groups is a rapidly diversifying field of mathematics and mathematical physics, originally launched by developments in theoretical physics and statistical mechanics involving quantum analogues of Lie algebras and coordinate rings of algebraic groups. The study of these objects and their representation theory has opened up important new directions in non-commutative algebra.
The aim of the course is to provide young researchers with the necessary tools to tackle open problems in the subject area, giving them the opportunity to learn the most recent results on the structure and representation theory of quantized coordinate rings and quantized enveloping algebras. The label "quantized coordinate ring" is used in the literature to refer to various non-communicative algebras which are, informally expressed, deformations of the classical coordinate rings of algebraic varieties or algebraic groups; the adjective "quantized" usually indicates that some solution to the quantum Yang-Baxter equation is involved in the construction and/or the representation theory of the algebra.
The known algebras that, by general agreement, carry the label "quantized coordinate rings" do share a substantial number of common features, which will be developed in the lectures. Similarly, quantum enveloping algebras of semi-simple, Lie algebras (or of affine Kac-Moody algebras). This class of algebras is somewhat more tightly defined; in that generators and relations are given by a standard process applied to the Serre relations for classical enveloping algebras. As in the classical setting, there is a duality between these algebras and the quantized coordinate rings of the corresponding semi-simple algebraic groups.
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 applied mathematics mathematical physics
- natural sciences mathematics pure mathematics algebra
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences physical sciences theoretical physics
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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.
Coordinator
SL3 9EG SLOUGH
United Kingdom
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