关于严格shod代数中IP路的钩子

On the Hooks in A IP Path for Shod Algebras

shod代数(小维数代数)是研究代数表示论的一种重要的代数类型,它包含严格shod代数与拟倾斜代数.本文通过探讨严格shod代数中的钩子,证明了严格shod代数中的IP路至少存在一个钩子,且至多存在两个连续的钩子.

Shod algebras（or algebras with small homological dimensions） is an important class of algebras for researching representation theory. It contains quasitilted algebras and strictly shod algebras. In this paper we argue the hooks about the strictly shod algebras, and prove that a IP path in this class of algebras has at least one hook, but at most two consecutive hooks.