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Almost split sequences in categories of representations of quivers


Author: Sverre O. Smal\o{}
Journal: Proc. Amer. Math. Soc. 129 (2001), 695-698
MSC (1991): Primary 16E10, 16G10, 16G20, 16P10
DOI: https://doi.org/10.1090/S0002-9939-00-05625-2
Published electronically: September 20, 2000
MathSciNet review: 1706973
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Abstract:

Let $k$ be a field and $Q$ a connected quiver. In this note it is proved that the category of finite dimensional representations of $Q$ over $k$ has almost split sequences if and only if $Q$ either is without oriented cycles or consists of a single oriented cycle.


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Additional Information

Sverre O. Smal\o{}
Affiliation: Institutt for Matematiske fag, NTNU, 7491 Trondheim, Norway
Email: sverresm@math.ntnu.no

DOI: https://doi.org/10.1090/S0002-9939-00-05625-2
Received by editor(s): April 20, 1999
Received by editor(s) in revised form: June 11, 1999
Published electronically: September 20, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society