| EPSRC Reference: |
GR/R69426/01 |
| Title: |
Poisson Structures Transverse to Coadjoint Orbits |
| Principal Investigator: |
Roberts, Professor M |
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| Department: |
Sch of Electronics & Physical Sciences |
| Organisation: |
University of Surrey |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 February 2002 |
Ends: |
30 September 2002 |
Value (£): |
4,271
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The dual g` of a Lie algebra has a natural Poisson structure, the symplectic leaves of which are the coadjoint orbits. The Poisson structure on g' induces local Poisson structures on submanifolds that are transverse to coadjoint orbits. Up to isomorphism these depend only on the coadjoint orbit. The aim of this project is to describe a number of aspects of these transverse Poisson structures when the Lie algebra g is semisimple. In this case the Jacobson-Morosov embedding theorem and sl(2) representation theory can be used to construct a special transverse affine subspace for each point in g' for which we have recently proved that the Poisson structure matrix is polynomial. We plan to extend the method to determine precisely the degrees of these polynomials (conjectured by Damianou and Cushman for sl(n)) and also to explore the rings of Casimir functions and other geometric properties of the transverse Poisson structures. Apart from their intrinsic interest, Poisson structures transverse to coadjoint orbits arise naturally in the stability theory of Hamiltonian relative equilibria and its anticipated that the results of this research will in particular lead to a better understanding of stability in the presence of non compact symmetry groups.
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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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| Date Materialised |
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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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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.surrey.ac.uk |