We investigate the weighted fusion category algebra *(<i>b</i>) of a block <i>b</i> of a finite group, which is defined by Markus Linckelmann based on the fusion system of the block <i>b</i> to reformulate Alperin’s weight conjecture. We present the definition and fundamental properties of the weighted fusion category algebras from the first principle. In particular, we give an alternative proof that they are quasi-hereditary, and show that they are Morita equivalent to their Ringel duals. We compute the structure of the weighted fusion category algebras of tame blocks and principal 2-blocks of GL<i><sub>n</sub></i>(<i>q</i>) explicitly in terms of their quivers with relations and compare them with that of the <i>q</i>-Schur algebras <i>S<sub>n</sub></i>(<i>q</i>) for <i>q</i> odd prime powers and <i>n</i> = 2,3. As a result, we find structural connections between them.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:446250 |
| Date | January 2008 |
| Creators | Park, Sejong |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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