相对同调与极大l-正交模
Relative homology and maximal l-orthogonal modules
摘要：
设$Ł$是Artin代数. Iyama证明了任意两个极大$l$ -正交模$M_1$和$M_2$的自同态环是等价的.他证明了$l=1$的猜想，并为$l>1$给出了$M_1$和$M_2$的一些正交条件，使得$\End_Ł(M_2)^\op$ - $\End_Ł(M_1)$ -双模$\Hom_Ł(M_2,M_1)$是倾斜的，这意味着环$\End_Ł(M_2)$和$\End_Ł(M_1)$是等价的（参见\cite{H}）。本文利用$Ł$ -模$M_1$和$M_2$的相关理论刻画了$\Hom_Ł(M_2,M_1)$形式的倾斜模，从而推广了Iyama的结果.
英文摘要：
Let $Ł$ be an artin algebra. Iyama conjectures that the endomorphism ring of any two maximal $l$-orthogonal modules, $M_1$ and $M_2$, are derived equivalent. He proves the conjecture for $l=1$, and for $l>1$ he gives some orthogonality condition on $M_1$ and $M_2$, such that the $\End_Ł(M_2)^\op$-$\End_Ł(M_1)$-bimodule $\Hom_Ł(M_2,M_1)$ is tilting, which implies that the rings $\End_Ł(M_2)$ and $\End_Ł(M_1)$ are derived equivalent (see \cite{H}). The purpose of this paper is to characterize tilting modules of the form $\Hom_Ł(M_2,M_1)$ in terms of the relative theories induced by the $Ł$-modules $M_1$ and $M_2$, thus getting a generilization of Iyama's result.
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