ADE型广义d-丛倾斜代数的Hall多项式

On the existence of Hall polynomials for representation-finite generalized d-cluster tilted algebras of ADE type

本文主要介绍了遗传代数的广义d-丛范畴,广义d-丛倾斜代数的定义和性质及其相应的伽罗瓦覆盖结论,还介绍了彭联刚教授,郭晋云教授给出的表示有限型的有限维代数的Hall多项式存在的一个判别引理,并利用这些覆盖结论和判别引理证明了ADE型广义d-丛(d≥2)倾斜代数具有Hall多项式.

In this paper, we mainly introduce the definitions and properties about the generalized d-cluster categories and the generalized d-cluster tilting algebras of hereditary algebras and the corresponding Galois covering results, we also show the lemma given by Professor Peng and Professor Guo which is used to judge whether the Hall polynomials of finite dimensional algebras of representation-finite exist. Then we show the existence of Hall polynomials for representation-finite generalized d-cluster tilted algebras of ADE type using these covering results and the lemma.