Quiver

Weight on a quiver

Let π‘˜ βˆˆβ„• and Ξ“ be a quiver with adjacency matrix 𝐴(Ξ“) =(π‘Žπ‘–π‘—)π‘Ÿπ‘–,𝑗=1. A π‘˜-weight is a positive integral π‘˜-eigenvector of 𝐴, graph i.e. 𝑣𝑖 βˆˆβ„• such that

π‘Ÿβˆ‘π‘—=1π‘Žπ‘–π‘—π‘£π‘—=π‘˜π‘£π‘–

A quiver is called π‘˜-weightable iff a π‘˜-weight exists.1

develop | en | SemBr

Footnotes

  1. 2021. Connectivity properties of McKay quivers ↩

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