论文标题
2-期淤积复合物的表示形式不变
The representation invariants of 2-term silting complexes
论文作者
论文摘要
令$ a $为字段$ k $上的有限维数代数，而$ \ textbf {p} $是$ k^{b}（\ text {proj} a）$中的2-期淤塞复合体。在本文中，我们使用淤积理论研究了$ \ text {end} _ {d^{b}（a）} $的表示维度。我们表明，如果$ \ textbf {p} $是具有某些同源限制的分离磨碎复合体，则rep.dim $ a = $ a = $ rep.dim $ \ text {end} _ {d^{b}（a）}（a）}（\ textbf {p}）$。这给出了Chen和Hu所示的代表维度的经典比较定理的适当概括。众所周知，$ \ text {h}^{0}（\ textbf {p}）$是倾斜$ a/\ text {ann} _ {a}（\ textbf {p}）$ - 模块。我们还显示rep.dim $ \ text {end} _ {a}（\ text {h}^{0}（\ textbf {p}））= $ rep.dim $ a/\ text {ann} _ {ann} _ {a} _ {a}（\ textbf {p}）
Let $A$ be a finite dimensional algebra over a field $k$ and $\textbf{P}$ be a 2-term silting complex in $K^{b}(\text{proj}A)$. In this paper, we investigate the representation dimension of $\text{End}_{D^{b}(A)} (\textbf{P})$ by using the silting theory. We show that if $\textbf{P}$ is a separating silting complex with certain homological restriction, then rep.dim $A=$rep.dim $\text{End}_{D^{b}(A)}(\textbf{P})$. This gives a proper generalization of the classical compare theorem of representation dimensions showed by Chen and Hu. It is well-known that $\text{H}^{0}(\textbf{P})$ is a tilting $A/\text{ann}_{A} (\textbf{P})$-module. We also show that rep.dim $\text{End}_{A} (\text{H}^{0}(\textbf{P})) = $rep.dim $A/\text{ann}_{A} (\textbf{P})$ if $\textbf{P}$ is a separating and splitting silting complex.
