Signed quivers, symmetric quivers, and root systems
Algebraic Geometry
2007-05-23 v1 Representation Theory
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.
Cite
@article{arxiv.math/0309091,
title = {Signed quivers, symmetric quivers, and root systems},
author = {D. A. Shmelkin},
journal= {arXiv preprint arXiv:math/0309091},
year = {2007}
}
Comments
20 pages