论文标题
三角矩阵代数中的特殊周期
Exceptional cycles in triangular matrix algebras
论文作者
论文摘要
带有SERRE函子的三角类别中的特殊周期是球形对象的概括。假设$ a $ and $ b $是戈伦斯坦代数，给定一个完美的$ n $ n $ -cycle $ e _*$ in $ k^b（a \ mbox { - } { - } {\ rm proj}）$，一个完美的异常$ $ m $ m $ m $ m $ -cycre $ f _*in $ k^b（b \ k^b（b \ mbox wer） $ a $ - $ b $ -bimodule $ n $，并证明产品$ e _*\ boxtimes f _*$是$ k^b（λ\ mbox { - } {\ mbox { - } {\ rm proj}）$ k^b（λ\ mbox {\ rm proj}）$ cyper in $ k^b（weny $λ= \λ= \ pmatrix {使用这种结构，人们获得了许多新的特殊周期，这些周期以前是某些类别的代数。
An exceptional cycle in a triangulated category with Serre functor is a generalization of a spherical object. Suppose that $A$ and $B$ are Gorenstein algebras, given a perfect exceptional $n$-cycle $E_*$ in $K^b(A\mbox{-}{\rm proj})$ and a perfect exceptional $m$-cycle $F_*$ in $K^b(B\mbox{-}{\rm proj})$, we construct an $A$-$B$-bimodule $N$, and prove the product $E_*\boxtimes F_*$ is an exceptional $(n+m-1)$-cycle in $K^b(Λ\mbox{-}{\rm proj})$, where $Λ=\begin{pmatrix}A & N\\ 0 & B \end{pmatrix}$. Using this construction, one gets many new exceptional cycles which is unknown before for certain class of algebras.
