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Gluing support τ-tilting modules via symmetric ladders of height 2

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Abstract

Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. In this paper, we present explicit constructions of gluing of support τ-tilting modules via symmetric ladders of height two. Moreover, we apply the result to triangular matrix algebras to give a detailed version of the known Jasso’s reduction and study maximal green sequences.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12201211) and the China Scholarship Council (Grant No. 202109710002). The author is grateful to Professor Dong Yang for his many helpful discussions. She also thanks Professor Xiaowu Chen and Professor Nan Gao for their several discussions. She thanks Professor Guodong Zhou for pointing out the reference [16]. Thanks also go to Professor Osamu Iyama for pointing out to the author that φ in the proof of Theorem 5.9 is injective and Dr. Peigen Cao for suggesting maximal green sequences. She thanks the support and excellent working conditions during her visit to Professor Osamu Iyama at the University of Tokyo. Moreover, she thanks referees for useful comments.

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  1. Department of Mathematics, Huzhou University, Huzhou, 313000, China

    Yingying Zhang

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  1. Yingying Zhang
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Zhang, Y. Gluing support τ-tilting modules via symmetric ladders of height 2. Sci. China Math. (2024). https://doi.org/10.1007/s11425-021-2154-x

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