导子商代数的稳定Calabi-Yau性质
Stably Calabi-Yau properties of derivation quotient algebras
摘要：
研究导子商代数的双模稳定Calabi-Yau性质。给出了扭稳定Calabi-Yau代数的定义，并证明了任何扭导子商代数$A$，若其双模复形给出了$A$的双模分解的开始，则它是双模稳定扭Calabi-Yau代数.在这种情况下，我们给出了余[Yu 12]的一些结果的新解释，即$A$几乎是周期型的Koszul.利用Amiot和Oppermann在[AO 14]中给出的高次预投射代数的特征，证明了具有齐次位势和正合伴随复形的有限维双阶导子商代数代数是其零次子代数的高次预投射代数，该零次子代数是Koszul和$(d-1)$ -表示有限的.
英文摘要：
The aim of this paper is to study bimodule stably Calabi-Yau properties of derivation quotient algebras. We give the definition of a twisted stably Calabi-Yau algebra and show that every twisted derivation quotient algebra $A$ for which the associated bimodule complex gives the beginning of a bimodule resolution for $A$ is bimodule stably twisted Calabi-Yau. In this setting we give a new interpretation of some results by Yu [Yu12], implying that $A$ is almost Koszul of periodic type. Using the characterization of higher preprojective algebras given by Amiot and Oppermann in [AO14], we prove that finite dimensional bigraded derivation quotient algebras with homogeneous potential and exact associated complex are higher preprojective algebras of their degree-zero subalgebra, which is Koszul and $(d-1)$-representation finite.
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