Graded Blocks of Group Algebras
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Thu, 06/05/2010 14:30 |
Dusko Bogdanic (Oxford) |
Representation Theory Seminar  |
L3 |
| We introduce the idea of transfer of gradings via derived equivalences and we apply it to construct positive gradings on a basic Brauer tree algebra corresponding to an arbitrary Brauer tree T. We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra, whose tree is a star. To transfer gradings via derived equivalence we use tilting complexes constructed by taking Green's walk around T. We also prove that there is a unique grading on an arbitrary Brauer tree algebra, up to graded Morita equivalence and rescaling. | |||