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On Simple-Minded Systems Over Representation-Finite Self-Injective Algebras

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Abstract

Let A be a representation-finite self-injective algebra over an algebraically closed field k. We give a new characterization for an orthogonal system in the stable module category A-\(\underline {\text {mod}}\) to be a simple-minded system. As a by-product, we show that every Nakayama-stable orthogonal system in A-\(\underline {\text {mod}}\) extends to a simple-minded system.

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Acknowledgements

The authors are supported by NSFC (No.12031014 and No.11971449). We would like to thank Steffen Koenig and Aaron Chan for comments and many suggestions on the presentation of this paper. We are grateful to the referee for valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Jing Guo

  2. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Yuming Liu & Zhen Zhang

  3. School of Mathematical Sciences, CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Yu Ye

  4. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Zhen Zhang

Authors
  1. Jing Guo
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  2. Yuming Liu
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  3. Yu Ye
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  4. Zhen Zhang
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Correspondence to Zhen Zhang.

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Presented by: Christof Geiss

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Guo, J., Liu, Y., Ye, Y. et al. On Simple-Minded Systems Over Representation-Finite Self-Injective Algebras. Algebr Represent Theor 25, 983–1002 (2022). https://doi.org/10.1007/s10468-021-10056-8

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  • DOI: https://doi.org/10.1007/s10468-021-10056-8

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