A note on singular equivalences and idempotents

@article{Shen2020ANO,
  title={A note on singular equivalences and idempotents},
  author={Dawei Shen},
  journal={arXiv: Representation Theory},
  year={2020}
}
  • Dawei Shen
  • Published 2020
  • Physics, Mathematics
  • arXiv: Representation Theory
Let $\Lambda$ be an Artin algebra and let $e$ be an idempotent in $\Lambda$. We study certain functors which preserve the singularity categories. Suppose $\mathrm{pd}\Lambda e_{e\Lambda e}<\infty$ and $\mathrm{id}_\Lambda\tfrac{\Lambda/\langle e\rangle}{\mathrm{rad}\Lambda/\langle e\rangle} < \infty$, we show that there is a singular equivalence between $e\Lambda e$ and $\Lambda$. 
Reduction techniques of singular equivalences

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