2024/05/30 by Huang, Xin
#20C20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2405.20268
We introduce a new type of equivalence between blocks of finite group algebras called an almost isotypy. An almost isotypy restricts to a weak isotypy in Broué's original definition, and it is slightly weaker than Linckelmann's version. We show that a bimodule of two block algebras of finite groups - which has an endopermutation module as a source and which induces a Morita equivalence - gives rise, via slash functors, to an almost isotypy if the character values of a (hence any) source are rational integers. Consequently, if two blocks are Morita equivalent via a bimodule with endopermutation source, then they are almost isotypic. We also explain why the notion of almost isotypies is reasonable.