MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS

MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS
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标准分层代数的有限投影维数模

DOI：
10.1081/agb-100001660
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
I. Reiten
I. Reiten
中科院分区：
--
文献类型：
--
作者：
M. Platzeck;I. Reiten

文献摘要

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本文研究标准层代数，它是拟遗传代数的推广。对于拟遗传代数，我们证明了存在一个自然地与具有Δ-滤子的模范畴F（Δ）相联系的倾斜模.我们用箭图的形式给出了F（Δ）与有限投射维数模范畴P <∞（Λ）相一致的充分条件，从而推广了以前的结果，并给出了P <∞（Λ）是反变有限的新的例子.证明了对于标准分层代数，F（Δ）的Grothendieck群的关系由几乎可裂序列生成.
This paper deals with standardly stratified algebras, a generalization of quasihereditary algebras. As for quasihereditary algebras we show that there is a tilting module naturally associated with the category F(Δ) of modules with Δ-filtration. We find sufficient conditions in terms of quivers with relations for F(Δ) to coincide with the category P <∞(Λ) of modules of finite projective dimension, thus generalizing earlier results and providing new classes of examples where P <∞(Λ) is contravariantly finite. We also prove that for a standardly stratified algebra the relations for the Grothendieck group for F(Δ) are generated by almost split sequences.