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Jiao, Pengjie

Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver. (English) Zbl 1429.16005

Forum Math. 31, No. 5, 1331-1349 (2019).
Summary: For an interval finite quiver \(Q\), we introduce a class of flat representations. We classify the indecomposable projective objects in the category \(\mathrm{rep}(Q)\) of pointwise finite dimensional representations. We show that an object in \(\mathrm{rep}(Q)\) is projective if and only if it is a direct sum of countably generated flat representations.

Cited in 1 Document

MSC:

16D40 Free, projective, and flat modules and ideals in associative algebras
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
16G20 Representations of quivers and partially ordered sets

Keywords:

interval finite quiver; flat representations; pointwise finite dimensional representations; projective objects
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References:

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