A non-existence theorem for almost split sequences

Details A non-existence theorem for almost split sequences A non-existence theorem for almost split sequences

2011-04-06

arxiv.org/abs/1104.1195v1

Mathematics

Representation Theory

8 pages

Scientific paper

Let k be a field, Q a quiver with countably many vertices and I an ideal of kQ such that kQ/I has finite dimensional Hom-spaces. In this note, we prove that there is no almost split sequence ending at an indecomposable not finitely presented representation of the bound quiver (Q,I). We then get that an indecomposable representation M of (Q,I) is the ending term of an almost split sequence if and only if it is finitely presented and not projective. The dual results are also true.

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