Bilkent Üniversitesi Cebir Seminerleri
Counting Wedderburn Components of Finite Group Algebras Over $Q_{p}$
Robert Boltje
University of California Santa Cruz, Amerika Birleşik Devletleri
Let $b$ be a block idempotent of the finite group algebra $Z_{p}G$. We present a conjecture that expresses the number of Wedderburn components of $Q_{p}G$ of a given "type" as an alternating sum of those numbers for blocks associated with $b$ on $p$-local subgroups. We prove that this conjecture is equivalent to a refinement of Alperin's weight conjecture due to Turull and that it holds for various classes of blocks. This is joint work with Burkhard Külshammer.
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