论文标题
Auslander-Reiten翻译何时在Grothendieck组上线性运行？ - 第一部分
When does the Auslander-Reiten translation operate linearly on the Grothendieck group? -- Part I
论文作者
论文摘要
对于遗传性，有限维代数$ a $ COXETER转换扩展了Auslander的作用 - 对非预设性不可兼容模块的重新翻译到有限生成的$ A $ -Modules类别的Grothendieck组的线性内态。自然要问其他代数是否接受类似的线性扩展。我们表明，所有Nakayama代数确实是这种情况。相反，我们表明，具有非囊性和连接的箭量承认这种线性扩展的有限维代数已经是循环nakayama代数。
For a hereditary, finite-dimensional algebra $A$ the Coxeter transformation extends the action of the Auslander--Reiten translation on the non-projective indecomposable modules to a linear endomorphism of the Grothendieck group of the category of finitely generated $A$-modules. It is natural to ask whether other algebras admit a similar linear extension. We show that this is indeed the case for all Nakayama algebras. Conversely, we show that finite-dimensional algebras with non-acyclic and connected quiver admitting such a linear extension are already cyclic Nakayama algebras.
