论文标题
强大的全球维度，量化尺寸的复合物和衍生类别之间的关系
Relations Between the Strong Global Dimension, Complexes of Fized Size and Derived Category
论文作者
论文摘要
令$ \ mathbb {z} $为整数数字，$ \ mathbb {k} $一个代数封闭的字段，$λ$ a有限尺寸$ \ mathbb {k} $ - mod $ up $λ$ $λ $λ$ -Modules和$ c_n（projλ）$投影型$λ$ - 固定尺寸的限制复合物，用于任何整数$ n \ geq2 $。我们找到了一种算法来计算$λ$的强大全局尺寸，当$λ$是使用类别的Auslander-Reiten Quivers $ C_N（PROJλ）$的有限的强度全球尺寸和衍生离散的算法。此外，我们还显示了有限的衍生类别的Auslander-Reiten Quiver $ d^b（λ）$与$ c_ {η+1}（projλ）$的Auslander-Reiten Quiver之间的关系，其中$η= s.gl.dim（λ）$（强大的全局压缩$λ$）。
Let $\mathbb{Z}$ be the integer numbers, $\mathbb{K}$ an algebraically closed field, $Λ$ a finite dimensional $\mathbb{K}$-algebra, mod$Λ$ the category of finitely generated right modules, proj$Λ$ the full subcategory of mod$Λ$ consisting of all projective $Λ$-modules, and $C_n(projΛ)$ the bounded complexes of projective $Λ$-modules of fixed size for any integer $n\geq2$. We find an algorithm to calculate the strong global dimension of $Λ$, when $Λ$ is a finite strong global dimension and derived discrete, using the Auslander-Reiten quivers of the categories $C_n(projΛ)$. Also, we show the relation between the Auslander-Reiten quiver of the bounded derived category $D^b(Λ)$ and the Auslander-Reiten quiver of $C_{η+1}(projΛ)$, where $η=s.gl.dim(Λ)$ (strong global dimension of $Λ$).
