Minimal algebras of infinite representation type with preprojective component
Minimal algebras of infinite representation type with preprojective component
复制标题
DOI：
10.1007/bf01169585
复制
发表时间：
1983-06
影响因子：
0.6
通讯作者：
D. Happel;D. Vossieck
中科院分区：
文献类型：
--
作者：
D. Happel;D. Vossieck
设 A 是代数闭域 k 上的有限维基本连通代数（结合，与 1）。用 e1,...,ena 表示 A 中原始正交幂等的完整集合，并用 Ai= A/AeiA 表示。如果 A 本身是无限表示类型，则 A 称为无限表示类型的最小代数，而所有 Ai（1≤i≤n）都是有限表示类型。主要结果给出了在 Auslander-Reiten 箭袋中具有预投影分量的最小代数的分类。通过认识到这些代数本质上是由驯服的遗传代数上的预投影倾斜模给出的，从而获得分类。
Let A be a finite dimensional, basic and connected algebra (associative, with 1) over an algebraically closed field k. Denote by e1,...,ena complete set of primitive orthogonal idempotents in A and by Ai= A/AeiA. A is called a minimal algebra of infinite representation type provided A is itself of infinite representation type,whereas all Ai, 1≤i≤n,are of finite representation type. The main result gives the classification of the minimal algebras having a preprojective component in their Auslander-Reiten quiver. The classification is obtained by realizing that these algebras are essentially given by preprojective tilting modules over tame hereditary algebras.