Calabi-Yau代数和非交换代数几何中若干相关问题的研究
基本信息
结项摘要
Calabi-Yau代数起源于代数几何和数学物理的研究：一个Calabi-Yau流形上的凝聚层的有界导出范畴上的Serre函子同构于移位函子的方幂。Kontsevich称具有这样性质的三角范畴为Calabi-Yau范畴，其相对应的代数称为Calabi-Yau代数。近几年来，Calabi-Yau现象与性质在其它各个不同的领域中相继被发现，例如，Cluster范畴被证明是2维Calabi-Yau范畴；一些Artin-Schelter正则代数同样被证明是Calabi-Yau代数。因此，Calabi-Yau代数已成为数学物理、代数几何和非交换代数领域中的热门研究课题之一。本课题主要研究问题有：应用A(∞)-方法对几个特殊箭图所对应的3维诺特分次Calabi-Yau代数的结构进行讨论；应用非交换Bernstein-Gelfand-Gelfand对应刻画3维Calabi-Yau代数的几何性质。
项目摘要
项目成果
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数据更新时间：2023-05-31
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