Objective
In global analysis or in algebraic geometry, a geometric space is described by an algebra of functions on this space. Non-commutative geometry extends this approach to geometry also to non-commutative algebras. In this way, A. Connes generalized in particular results from index theory and spin geometry. The aim of this project is to apply the methods of non-commutative geometry to so-called quantum homogeneous spaces. There are several definitions of this notion, but all of them cover a class of algebras that are obtained by quantizing the irreducible generalized flag manifolds (the irreducible compact Hermitian symmetric spaces) with respect to some Poisson bracket. For these, the proposer constructed a Dirac operator fitting into Connes and apos; concept o f a spectral triple (a non-commutative analogue of spin manifolds). Now, the main objective is to investigate quantum homogeneous spaces focusing on homological aspects.
The goal is also to extend the aforementioned construction of Dirac operators for quantum flag manifolds to a larger class of quantum homogeneous spaces, and to study the algebraic properties of analogues of Clifford algebras that were involved in obtaining these Dirac operators. One of the motivations of non-commutative geometry is to make assertions about physical models in the non-commutative setting. A long-term objective of this project is to formulate and study Yang-Mills theory on quantum homogeneous spaces. P.M. Hajac, the researcher in charge at the host institution (IMPAN), has worked on such topics for about a decade and made some significant contributions to the subject. There are several groups at IMPAN and the University of Warsaw that work on related topics. Finally, the planned Transfer of Knowledge grant and quot; Non-commutative Geometry and Quantum Groups and quot; will bring some of the world and apos;s leading experts to Warsaw. Hence the proposer considers Warsaw a very good place for carrying out this project.
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 geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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
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
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
WARSZAWA
Poland
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.