Derived representation type and field extensions
Derived representation type and field extensions
复制标题
派生的制图表达类型和字段扩展
DOI：
10.4064/cm8376-3-2021
复制
发表时间：
2020-03
影响因子：
0.4
通讯作者：
Jie Li;Chao Zhang
中科院分区：
文献类型：
--
作者：
Jie Li;Chao Zhang
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 complexes of projective $A$-modules. $\mathbf{C}$-dichotomy implies the dichotomy properties of representation type on the levels of homotopy category and derived category. 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.
