Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446250
Title: The weighted fusion category algebra
Author: Park, Sejong
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2008
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Abstract:
We investigate the weighted fusion category algebra *(b) of a block b of a finite group, which is defined by Markus Linckelmann based on the fusion system of the block b 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 GLn(q) explicitly in terms of their quivers with relations and compare them with that of the q-Schur algebras Sn(q) for q odd prime powers and n = 2,3.  As a result, we find structural connections between them.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.446250  DOI: Not available
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