论文标题
派生的表示类型和现场扩展
Derived Representation Type and Field Extensions
论文作者
论文摘要
让$ a $成为field $ k $的有限维代数。我们将$ a $定义为$ \ mathbf {c} $ - 二分法（如果它具有代表性类型的二分法属性，则在投影$ a $ a $模型的复合体上。 $ \ mathbf {c} $ - 二分法意味着表示类型的二分法在同型类别和派生类别的水平上。如果$ k $承认有限的可分离字段扩展名$ k/k $，这样$ k $是代数关闭的，则实际数字字段，我们证明$ a $是$ \ mathbf {c} $ - dichotomic。结果，第二个派生的brauer-thrall type定理以$ a $（即$ a $是衍生的离散或强烈派生的无限源）为生。
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.
