Isotypic blocks of finite groups algebras that are not p-permutation equivalent

2025/06/03 by McHugh, John Revere
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.03446

Abstract

We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a p-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not p-permutation equivalent. These results help to clarify the distinction between a p-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a p-permutation equivalence.

Citations

• p-permutation equivalences between blocks of group algebras
• On isotypies between Galois conjugate blocks

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• On Morita equivalences with endopermutation source and isotypies
• Isotypic blocks are functorially equivalent
• A note on blocks of finite groups with TI Sylow p-subgroups
• Galois descent of equivalences between blocks of p-nilpotent groups