Realizing stable categories as derived categories
Realizing stable categories as derived categories
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DOI：
10.1016/j.aim.2013.08.017
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发表时间：
2012-01
影响因子：
1.7
通讯作者：
K. Yamaura
中科院分区：
文献类型：
--
作者：
K. Yamaura
本文讨论了分次自内射代数的表示论与有限整体维数代数的表示论之间的关系。对于正分次自内射代数A，使得A0具有有限的整体维数，我们构造了两类三角等价。首先证明了Z-分次A-模的稳定范畴与有限整体维数代数Γ的导范畴之间存在三角等价。其次，证明了若A具有Gorenstein参数λ，则Z/λ Z-分次A-模的稳定范畴与Γ的导轨范畴之间存在三角等价，导轨范畴是导轨范畴的三角化船体.
In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra A such that A 0 has finite global dimension, we construct two types of triangle-equivalences. First we show that there exists a triangle-equivalence between the stable category of Z-graded A-modules and the derived category of a certain algebra Γ of finite global dimension. Secondly we show that if A has Gorenstein parameter ℓ, then there exists a triangle-equivalence between the stable category of Z/ℓ Z-graded A-modules and a derived-orbit category of Γ, which is a triangulated hull of the orbit category of the derived category.