Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver
Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver
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DOI：
10.1515/forum-2018-0196
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发表时间：
2018-04
影响因子：
0.8
通讯作者：
Pengjie Jiao
中科院分区：
文献类型：
--
作者：
Pengjie Jiao
摘要对于区间有限的非线性代数Q，我们引入了一类平坦表示。我们将不可分解的射影对象分类到有限维逐点表示的范畴rep（Q）{\mathrm{rep}（Q）}中。我们证明了一个对象在rep（Q）{\mathrm{rep}（Q）}中是投射的当且仅当它是可数生成的平坦表示的直和。
Abstract For an interval finite quiver Q, we introduce a class of flat representations. We classify the indecomposable projective objects in the category rep ( Q ) {\mathrm{rep}(Q)} of pointwise finite dimensional representations. We show that an object in rep ( Q ) {\mathrm{rep}(Q)} is projective if and only if it is a direct sum of countably generated flat representations.