On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras

@article{Koshitani2019OnTO,
  title={On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras},
  author={Shigeo Koshitani and Taro Sakurai},
  journal={Archiv der Mathematik},
  year={2019},
  volume={113},
  pages={1-10}
}
In 1941, Brauer-Nesbitt established a characterization of a block with trivial defect group as a block B with $$k(B) = 1$$k(B)=1 where k(B) is the number of irreducible ordinary characters of B. In 1982, Brandt established a characterization of a block with defect group of order two as a block B with $$k(B) = 2$$k(B)=2. These correspond to the cases when the block is Morita equivalent to the one-dimensional algebra and to the non-semisimple two-dimensional algebra, respectively. In this paper… Expand
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