Objective
The subject of Quantum Groups and Quantum Algebras developed out of ideas in physics in the 80s. Subsequently, the range of applications in physics, and their pivotal role in several areas of mathematics has lead to this subject being one of the most active in mathematics. From an algebraic point of view, it has recently become apparent that the subject should be studied as part of the developing theory of Non-commutative Geometry. In this theory, the non-commutative algebras arising from deformations of the classical commutative case are studied by algebraic means, but from a geometrical perspective. This development is somewhat akin to the development in physics of Quantum Mechanics as a non-commutative deformation of the classical Newtonian view of physics - the non-commutativity reflecting the uncertainty principle.
From this point of view, the 'points', 'curves', 'surfaces', etc. in classical geometry are replaced in non-commutative geometry by the prime and primitive spectra and the representation theory of the algebras. The most important algebras that arise in this study are the quantum coordinate algebras and quantum enveloping algebras arising from the classical groups and the algebra of quantum matrices. Important tasks are to understand the prime spectra, to calculate automorphism groups and to understand the poisson structure that the classical world inherits from the quantum world.
These are the main tasks involved in this proposal. The tasks are interlinked. In contrast with their classical counterparts, the quantum deformations are much more rigid objects (at least in the generic case) and this is reflected by the relatively small size of the so-called H-prime spectrum of these algebras. This in turn puts restrictions on the possible automorphisms of the algebras and should lead to much smaller automorphism groups. The poisson structure in the classical case should then be linked in a natural way to the corresponding quantum features.
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 physical sciences quantum physics
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
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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)
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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.
FP6-2002-MOBILITY-5
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Funding Scheme
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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
United Kingdom
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.