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Homological Transfer between Additive Categories and Higher Differential Additive Categories

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Abstract

Given an additive category \({\cal C}\) and an integer n ≥ 2. The higher differential additive category consists of objects X in \({\cal C}\) equipped with an endomorphism ϵX satisfying \(\epsilon_X^n = 0\). Let R be a finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(tn)-modules. It is proved that a finitely generated left R-module M is τ-rigid (respectively, (support) τ-tilting, almost complete τ-tilting) if and only if so is T(M)as a left R[t]/(tn)-module. Moreover, R is τm-selfinjective if and only if so is R[t]/(tn).

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Science, Guilin University of Aerospace Technology, Guilin, 541004, P. R. China

    Xi Tang

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

    Zhao Yong Huang

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  1. Xi Tang
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  2. Zhao Yong Huang
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Correspondence to Zhao Yong Huang.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

Supported by NSFC (Grant Nos. 12371038, 11971225, 12171207, 12061026) and NSF of Guangxi Province of China (Grant No. 2020GXNSFAA159120)

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Tang, X., Huang, Z.Y. Homological Transfer between Additive Categories and Higher Differential Additive Categories. Acta. Math. Sin.-English Ser. (2023). https://doi.org/10.1007/s10114-023-2193-8

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  • DOI: https://doi.org/10.1007/s10114-023-2193-8

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