The Auslander-Reiten Components in the Rhombic Picture

Details The Auslander-Reiten Components in the Rhombic Picture The Auslander-Reiten Components in the Rhombic Picture

2012-04-07

arxiv.org/abs/1204.1654v1

Mathematics

Representation Theory

28 pages, 6 figures

Scientific paper

For an indecomposable module $M$ over a path algebra of a quiver of type
$\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new
numerical invariants; we call them the multiplicity, and the initial, periodic
and final parts. We describe how these invariants for $M$ and for its dual
specify the position of $M$ in the Auslander-Reiten quiver of the algebra.

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