Trace and defect of a block idempotent
The author gives a new proof of R. Brauer's result that the p-part of the dimension of a block algebra B in prime characteristic p is \(p^{2a-d}\) where \(p^ a\) is the p-part of the order of G and d is the defect of B. The proof is based on the known structure of blocks with normal defect groups and the Green correspondence. An application shows that 1 appears in the support of the block idempotent of B if and only if B has maximal defect.
scientific article; zbMATH DE number 4146232