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Signed quivers, symmetric quivers, and root systems

D. A. Shmelkin
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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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D. A. Shmelkin. 2003-09-05. Signed quivers, symmetric quivers, and root systems. https://arxiv.org/abs/math/0309091

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