Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

@article{Koshitani2017SplendidME,
  title={Splendid Morita equivalences for principal 2-blocks with dihedral defect groups},
  author={Shigeo Koshitani and Caroline Lassueur},
  journal={Mathematische Zeitschrift},
  year={2017},
  volume={294},
  pages={639-666}
}
  • Shigeo Koshitani, Caroline Lassueur
  • Published 2017
  • Mathematics
  • Mathematische Zeitschrift
  • Given a dihedral 2-group P of order at least 8, we classify the splendid Morita equivalence classes of principal 2-blocks with defect groups isomorphic to P. To this end we construct explicit stable equivalences of Morita type induced by specific Scott modules using Brauer indecomposability and gluing methods; we then determine when these stable equivalences are actually Morita equivalences, and hence automatically splendid Morita equivalences. Finally, we compute the generalised decomposition… CONTINUE READING

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