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Two terms tilting complexes and Ringel–Hall algebras

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Abstract

In this paper, we show that under certain mild assumptions, each 2-term silting complex induces isomorphisms between certain subalgebras of Ringel–Hall algebras. This result generalizes the earlier result about classic tilting modules to the silting complexes. Note that 2-term silting complexes are closely related to the support \(\tau \)-tilting modules. We also give the \(\tau \)-tilting version of Obul’s work.

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Acknowledgements

The author would like to express his gratitude to the referee for carefully reading the manuscript and for many valuable suggestions, which improved the presentation of this paper. The author also would like to thank Professor Bangming Deng for his comments and suggestions. The author was supported by the National Natural Science Foundation of China (Grant Nos 11971255 and 12071120).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Bei**g, 100084, People’s Republic of China

    Yonggang Hu

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  1. Yonggang Hu
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Correspondence to Yonggang Hu.

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Communicated by Manoj K. Keshari.

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Hu, Y. Two terms tilting complexes and Ringel–Hall algebras. Proc Math Sci 132, 70 (2022). https://doi.org/10.1007/s12044-022-00709-z

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  • DOI: https://doi.org/10.1007/s12044-022-00709-z

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