| EPSRC Reference: |
GR/R70057/01 |
| Title: |
Derived equivalent blocks of a group algebra |
| Principal Investigator: |
Chuang, Professor J |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Fast Stream |
| Starts: |
01 October 2001 |
Ends: |
30 September 2004 |
Value (£): |
58,828
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Broue's abelian defect group conjecture is one of the most important and intriguing open problems in the representation theory of finite groups. It uses the language of triangulated categories to make a succinct and beautiful prediction, giving a structural explanation for earlier numerical conjectures, such as Alperin's weight conjecture. It is the starting point for a homological framework for local representation theory.There has been a lot of progress in the last few years in proving Broue's conjecture, both in verifying particular cases and in developing general strategies. One consequence of this recent work has been the discovery of unexpected self -equivalences of the derived categories of group algebras which interchange blocks. The purpose of the proposed project is to fully explore these equivalences and to develop a suitable context for studyingsimilar examples. These equivalences are not only interesting in their own right but may also provide insight into Broue's conjecture as well as into the key problem of generalising the conjecture to the nonabelian case.
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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.bris.ac.uk |