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The Number of Two-Term Tilting Complexes over Symmetric Algebras with Radical Cube Zero

Annals of Combinatorics (2022)Cite this article

Abstract

In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. First, we give a complete list of symmetric algebras with radical cube zero having only finitely many isomorphism classes of two-term tilting complexes in terms of their associated graphs. Secondly, we enumerate the number of two-term tilting complexes for each case in the list.

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Acknowledgements

T. Adachi is supported by JSPS KAKENHI Grant Number JP17J05537. T. Aoki is supported by JSPS KAKENHI Grant Number JP19J11408. The authors would like to thank M. Konishi for helpful discussions about the proof of Proposition 4.1.

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Authors and Affiliations

  1. Faculty of Global and Science Studies, Yamaguchi University, 1677-1 Yoshida, Yamaguchi, 753-8541, Japan

    Takahide Adachi

  2. Graduate School of Mathematics, Nagoya University, Frocho, Chikusaku, Nagoya, 464-8602, Japan

    Toshitaka Aoki

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  1. Takahide Adachi
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  2. Toshitaka Aoki
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Correspondence to Takahide Adachi.

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Adachi, T., Aoki, T. The Number of Two-Term Tilting Complexes over Symmetric Algebras with Radical Cube Zero. Ann. Comb. (2022). https://doi.org/10.1007/s00026-022-00587-2

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  • DOI: https://doi.org/10.1007/s00026-022-00587-2