Quiver representations respecting a quiver automorphism: a generalisation of a theorem of Kac

Details Quiver representations respecting a quiver automorphism: a generalisation of a theorem of Kac Quiver representations respecting a quiver automorphism: a generalisation of a theorem of Kac

2002-03-19

arxiv.org/abs/math/0203195v2

Mathematics

Representation Theory

corrected typos; more transparent arguments in sections 4 and 6

Scientific paper

We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie algebra arises in this way. We also discuss the relationship with species of valued quivers over finite fields.

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