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Title: The weighted fusion category algebra
Author: Park, Sejong
ISNI:       0000 0001 3468 4699
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2008
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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:  DOI: Not available