论文标题
预选代数的等效定义
Equivalent definitions of the preprojective algebra
论文作者
论文摘要
在C. M. Ringel的文章之后，我们介绍了Dynkin Quiver $ Q $的前置代数，从三个定义开始，尽管这些定义完全不同，但事实证明这是同等的。我们的主要结果是林格尔的证明的新版本，该版本应用于Happel的定理，并利用同源代数的技术。此外，我们表明，以通常的换向器概念给出的前介绍性代数的定义等同于用“广义”换向器的定义。
Following the article of C. M. Ringel we introduce preprojective algebras of a Dynkin quiver $Q$ starting from three definitions which, despite concerning completely different algebraic structures, turn out to be equivalent. Our main result is a new version of Ringel's proofs that applies a theorem by Happel and exploits the techniques of homological algebra. Moreover we show that the definition of the preprojective algebra given with the usual notion of commutator is equivalent to the definition with the "generalised" commutator.
