| EPSRC Reference: |
EP/H02283X/2 |
| Title: |
Unitary forms of Kac-Moody algebras and Kac-Moody groups |
| Principal Investigator: |
Koehl, Professor R |
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| Department: |
Institute of Mathematics |
| Organisation: |
Justus-Liebig University Giessen |
| Scheme: |
Standard Research |
| Starts: |
30 June 2011 |
Ends: |
29 April 2014 |
Value (£): |
118,271
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Existing cosmological theories suggest that, close to a cosmological singularity like a big-bang or a big-crunch, the description of the universe in terms of spatial continuum and space-time based quantum field theory breaks down and the information encoded in the spatial variation of the geometryof the universe gets transferred into spatially independent but time-dependent Lie-algebraic variables encoded in the infinite-dimensional symmetric space of a real split Kac-Moody algebra over its unitary form. In this context the understanding of representations of the unitary form of the real split Kac-Moody algebra of so-called type E10 is of particular interest. One such representation can be constructed as an extension to the whole unitary form of the 32-dimensional spin representation of its regular subalgebra of type A9, using a presentation by generators and relations of unitary forms given by Berman.This project is set in pure mathematics within the areas of infinite-dimensional Lie theory and geometric group theory. It will combine classical techniques from the theory of Kac-Moody algebras and Kac-Moody groups in characteristic 0 and their unitary forms with the quickly developing theory of unitary forms of Kac-Moody groups over arbitrary fields based on the theory of twin buildings. Its goal is to contribute to a uniform structure theory of unitary forms of Kac-Moody algebras and of Kac-Moody groups of indefinite type. The main emphasis of this project will be on finite-dimensional representations and on ideals and normal subgroups, respectively, of these unitary forms, starting with the above-mentioned finite-dimensional representation discovered in cosmology.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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