论文标题
占主导地位的奥斯兰德 - 戈伦斯坦代数和混合集群倾斜
Dominant Auslander-Gorenstein algebras and mixed cluster tilting
论文作者
论文摘要
我们介绍了主要的Auslander-Gorenstein代数的类别，作为对高级Auslander代数和最小的Auslander-Gorenstein代数的概括，并赋予其基本特性。我们还引入了混合（前）集群倾斜模块作为（前）集群倾斜模块的概括，并通过证明优势auslander-Gorenstein（分别是Auslander-rgular-grounder）代数与混合倒数前（分别为ofertement，cluster）倾斜模块来建立Auslander型对应关系。我们表明，每个微不足道的扩展代数$ t（a）$ t $ d $ - 代表 - 代表代数A承认一个混合的集群倾斜模块，并表明这可以看作是众所周知的概括结果，结果$ d $ d $ pressentation-presentation-Finite-Finite代数是分量的Calabi-yau。我们表明，迭代的SGC扩展是Gendo对称占主导地位的Auslander-Gorenstein代数的迭代延期，该代数接纳了混合的混合簇倾斜模块。
We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also introduce mixed (pre)cluster tilting modules as a generalisation of (pre)cluster tilting modules, and establish an Auslander type correspondence by showing that dominant Auslander-Gorenstein (respectively, Auslander-regular) algebras correspond bijectively with mixed precluster (respectively, cluster) tilting modules. We show that every trivial extension algebra $T(A)$ of a $d$-representation-finite algebra A admits a mixed cluster tilting module and show that this can be seen as a generalisation of the well known result that $d$-representation-finite algebras are fractionally Calabi-Yau. We show that iterated SGC-extensions of a gendo-symmetric dominant Auslander-Gorenstein algebra admit mixed precluster tilting modules.
