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Singular Equivalences Induced by Bimodules and Quadratic Monomial Algebras

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Abstract

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between the homotopy categories of acyclic complexes of injective modules. We give conditions on when a bimodule appears in a pair of bimodules, that defines a singular equivalence with level. We construct an explicit bimodule in a combinatorial manner, which yields a singular equivalence between a quadratic monomial algebra and its associated algebra with radical square zero. Under certain conditions which include the Gorenstein cases, the bimodule does appear in a pair of bimodules defining a singular equivalence with level.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The first author thanks Bernhard Keller and Zhengfang Wang for helpful discussion. This work is supported by National Natural Science Foundation of China (No.s 11671245,11971449, and 11901551).

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Authors and Affiliations

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

    Xiao-Wu Chen, Jian Liu & Ren Wang

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  1. Xiao-Wu Chen
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  2. Jian Liu
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  3. Ren Wang
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Correspondence to Ren Wang.

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Presented by: Michela Varagnolo

Dedicated to Professor Pu Zhang on the occasion of his sixtieth birthday

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Chen, XW., Liu, J. & Wang, R. Singular Equivalences Induced by Bimodules and Quadratic Monomial Algebras. Algebr Represent Theor 26, 609–630 (2023). https://doi.org/10.1007/s10468-021-10104-3

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  • DOI: https://doi.org/10.1007/s10468-021-10104-3

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