Reducing Homological Conjectures by n-Recollements
Reducing Homological Conjectures by n-Recollements
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DOI：
10.1007/s10468-015-9578-z
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发表时间：
2015-11
影响因子：
0.6
通讯作者：
Yongyun Qin;Yang Han
中科院分区：
文献类型：
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作者：
Yongyun Qin;Yang Han
引入了三角范畴的n-元和n-导单代数。阐明了代数导出范畴的then-元分别与代数的Cartan行列式、同调光滑性和Gorensteinness之间的关系。作为应用，将Cartan行列式猜想约化为1-导单代数，将Gorenstein对称性猜想约化为2-导单代数。
n-recollements of triangulated categories andn-derived-simple algebras are introduced. The relations between then-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry conjecture is reduced to 2-derived-simple algebras.