2005/02/08 by D. A. Shmelkin, Shmelkin, D. A.
Mathematics · #14L30 #16G20 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30 #msc:16G20
paper · pdf · doi:10.48550/arxiv.math/0502156
19 pages
arxiv created 2005/02/08 · openalex publication_date 2005/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.