| EPSRC Reference: |
EP/D077656/1 |
| Title: |
Hecke algebras and self-injective algebras: varieties of modules and applications |
| Principal Investigator: |
Erdmann, Dr K |
| Other Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research |
| Starts: |
01 October 2006 |
Ends: |
30 June 2010 |
Value (£): |
253,733
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Representation theory studies how collections of linear transformations act on vector spaces, in other words it studies symmetries and related structures. When the linear transformations are invertible they represent a group, and this models symmetry. Algebras are more general, they also model processes which cannot be reversed. An example for such model is a linear transformation whose iteration eventually maps everything to zero. Another example comes from taking derivatives of functions- if x^2 is differentiated three times one gets zero. Hecke algebras belong to the larger class of cellular algebras which occur in many situations, such as in theoretical physics. One wants to have a mathematical model of phase transition; for example, water is very different from ice, although they have the same molecules. How can one understand this? Such processes are a motivation to study cellular algebras, but apart from this, they are very interesting mathematical objects. This project aims to investigate large-scale behaviour in the representation theory of Hecke algebras and related algebras.
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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 |
| Summary |
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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.ox.ac.uk |