CORELG
Computation with real Lie Groups
| Coordinatore | UNIVERSITA DEGLI STUDI DI TRENTO
Organization address
address: VIA CALEPINA 14 contact info |
| Nazionalità Coordinatore | Italy [IT] |
| Totale costo | 180˙912 € |
| EC contributo | 180˙912 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2010-IEF |
| Funding Scheme | MC-IEF |
| Anno di inizio | 2011 |
| Periodo (anno-mese-giorno) | 2011-10-01 - 2013-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITA DEGLI STUDI DI TRENTO
Organization address
address: VIA CALEPINA 14 contact info |
IT (TRENTO) | coordinator | 180˙912.00 |
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Obiettivo del progetto (Objective)
'Group theory is the mathematical discipline that deals with the systematic study of symmetry. Lie groups are used to describe some of the most complex forms of symmetry. Therefore they find many applications in various diverse areas such as physics and geometry. Since the invention of the computer, it has been used as a tool in the study of group theory and, in particular, Lie groups. This has led to a new research area, called Computational Lie Theory. The main focus in this area has been on complex Lie groups. However, it would be of great interest to use the computer to study real Lie groups because of the abundance of applications that these groups have in physics and differential geometry. It is the aim of the project 'Computation with Real Lie Groups' (CoReLG) to start such a development in Europe. In the U.S.A. a similar project has been set up, called the ATLAS project. In 2007 this project had a huge success, widely reported in the international press, when the so-called Kazhdan-Lusztig-Vogan polynomials were determined for the real Lie group of type E8. The project CoReLG aims at starting a similar research project in Europe. However, the research goals of the CoReLG project are genuinely different from those of the ATLAS project. The main objective will be to develop algorithms for one of the main problems regarding Lie groups: obtaining their orbits. As this problem is intractable in general, we focus on a special class of Lie groups, namely real theta-groups, which contain many instances of interest. Furthermore, the project aims at implementing these algorithms as a software package for a European public domain computer algebra system, such as GAP. A third goal of the proposed project is to develop applications of the algorithms in differential geometry and theoretical physics. This will be carried out in collaboration with several European differential geometers and physicists.'