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Derived representation type and field extensions

Volume 168 / 2022

Jie Li, Chao Zhang Colloquium Mathematicum 168 (2022), 105-117 MSC: Primary 16G10; Secondary 16E35. DOI: 10.4064/cm8376-3-2021 Published online: 6 October 2021


Let $A$ be a finite-dimensional algebra over a field $k$. We define $A$ to be $\mathbf C$-dichotomic if it has the dichotomy property of the representation type on the category of certain bounded complexes of projective $A$-modules. If $k$ admits a finite separable field extension $K/k$ such that $K$ is algebraically closed (the real number field for example), we prove that $A$ is $\mathbf C$-dichotomic. As a consequence, the second derived Brauer–Thrall type theorem holds for $A$, i.e., $A$ is either derived-discrete or strongly derived-unbounded.


  • Jie LiDepartment of Mathematics
    University of Science and Technology of China
    Hefei, Anhui, P.R. China
  • Chao ZhangDepartment of Mathematics
    School of Mathematics and Statistics
    Guizhou University
    550025, Guiyang, Guizhou, P.R. China

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