An observation on the module structure of block algebras

2018/04/22 by Gelvin, Matthew
#20C20 #20D20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1804.08158

Abstract

Let B be a p-block of the finite group G. We observe that the p-fusion of G constrains the module structure of B: Any basis of B that is invariant under the left and right multiplications of a chosen Sylow p-subgroup S of G must in fact form a semicharacteristic biset for the fusion system on S induced by G. The parameterization of such semicharacteristic bisets can then be applied to relate the module structure and defect theory of B.

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