Signed quivers, symmetric quivers, and root systems

2003/09/05 by D. A. Shmelkin, Shmelkin, D. A.
Mathematics · #14L30 #16G20 #17B67 #20G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30 #msc:16G20 #msc:17B67 #msc:20G20

paper · pdf · doi:10.48550/arxiv.math/0309091

20 pages

arxiv created 2003/09/05 · arxiv updated 2009/12/01

Abstract

We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of symmetric quivers, in particular we describe the indecomposable symmetric representations. Their dimensions constitute root systems corresponding to certain symmetrizable generalized Cartan matrices.

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