一个非平凡的Calabi-Yau DG代数  

A nontrivial Calabi-Yau DG algebra

作　　者：叶成成 毛雪峰[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2015年第1期115-126,共12页Communication on Applied Mathematics and Computation

摘　　要：证明例1中的DG代数不仅是Koszul,同调光滑DG代数,而且还是一个Calabi-Yau DG代数.该例子说明一个Calabi-Yau DG代数的同调分次代数不一定具有Calabi-Yau性质,甚至可能不是同调光滑的;另外,该例子还说明一个Calabi-Yau DG代数忘掉微分后得到的分次代数不一定是分次Calabi-Yau代数.It is proved that the DG algebra in Example 1 is not only a Koszul, homologically smooth DG algebra, but also a Calabi-Yau DG algebra. The example indicates that the cohomology algebra of a Calabi-Yau DG algebra may not have Calabi-Yau property, and it is even possible to be not homologically smoooth. Morever, the example also implies that the underlying graded algebra of a Calabi- Yau DG algebra may not be a graded Calabi-Yau algebra.

关 键 词：微分分次代数 Calabi—Yau 同调光滑 

分 类 号：O153.3[理学—数学]