| EPSRC Reference: |
GR/S35387/01 |
| Title: |
Actions of the Braid Group on Derived Categories of Representations of Simple Lie Algebras |
| Principal Investigator: |
Marsh, Professor BR |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 June 2004 |
Ends: |
30 November 2007 |
Value (£): |
144,018
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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A group is a way of measuring the symmetries of an object. For example a square has a symmetry group with 8 elements: 4 reflections and 4 rotations (including 0 degrees). A braid is a way of twisting strings around each other, and the collection of all braids forms a group. Its natural definition means that it is prevalent in many areas of mathematics. Symmetry also plays a role in the more abstract setting of algebras, which are spaces in which elements can also be multiplied; natural examples include spaces of matrices (arrays of numbers). In order to understand an algebra, it is useful to represent it by transformations. The links between different representations can be studied via the derived category associated to the algebra. In some cases, the braid group is known to be the symmetry group of the derived category of an algebra, but it is not really understood why. We aim to use the Category O (from Lie theory) to construct and understand such examples, employing Marsh's experience in canonical bases, Koenig's expertise in derived categories, and Stroppel's expertise in category O, while at the same time deepening the understanding of the Category O itself. The requested funds are for employment of the research assistant (Stroppel) and to cover meetings with experts in the field and dissemination.
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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: |
http://www1.maths.leeds.ac.uk/~marsh/epsrcproject2.html |
| Further Information: |
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| Organisation Website: |
http://www.le.ac.uk |