Locally semi-simple representations of quivers

Details Locally semi-simple representations of quivers Locally semi-simple representations of quivers

2005-02-08

arxiv.org/abs/math/0502156v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We suggest a geometrical approach to the semi-invariants of quivers based on Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple representations are defined in this spirit but turn out to be connected with stable representations in the sense of GIT, Schofield's perpendicular categories, and Ringel's regular representations. As an application of this method we obtain an independent short proof of the theorem of Skowronsky and Weyman about semi-invariants of the tame quivers.

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