Brauer graph algebras are closed under stable equivalence of Morita type

@misc{chen2026brauer,
  title = {{Brauer graph algebras are closed under stable equivalence of Morita type}},
  author = {Pengyun Chen and Nengqun Li and Yuming Liu and Bohan Xing},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.14253},
  eprint = {2608.14253},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.14253},
}

TY  - UNPB
TI  - Brauer graph algebras are closed under stable equivalence of Morita type
AU  - Pengyun Chen
AU  - Nengqun Li
AU  - Yuming Liu
AU  - Bohan Xing
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.14253
UR  - https://arxiv.org/abs/2608.14253
AB  - We study stable equivalences of Brauer graph algebras. We prove that a basic symmetric algebra without semisimple summands which is stably equivalent to a Brauer graph algebra is again a Brauer graph algebra. In particular, Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type. As consequences, we reprove the closure under derived equivalence established by Antipov and Zvonareva and obtain a solution of the reconstruction problem posed by Rickard and Rouquier for algebras stably equivalent of Morita type to Brauer graph algebras.
ER  -