Locally semi-simple representations of quivers

D. A. Shmelkin

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arXiv · math/0502156

Locally semi-simple representations of quivers

D. A. Shmelkin

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Abstract

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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BibTeX RIS

D. A. Shmelkin. 2005-02-08. Locally semi-simple representations of quivers. https://arxiv.org/abs/math/0502156

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