QuiverPath

A directed path in a quiver: where it starts, and the arrow indices it follows. The basis of the path algebra , with one trivial path per vertex.

WikipediaQuiver (mathematics)↗WikidataQ493980↗Encyclopedia of MathematicsQuiver↗nLabquiver↗

QuiverPath(v, [])the trivial path at vertex — a local identity

QuiverPath(v, [i, j, …])the path from along arrows , , …

Domain: Path algebras

Details

• Arrows are indexed by position in the quiver's arrow list, so PARALLEL arrows are distinct basis elements
• Composition is QuiverCompose, which needs the quiver: a path alone does not know which quiver it belongs to
• The trivial paths are local identities:
• Quivers: `LinearQuiver(n)` (), `JordanQuiver` (one loop), `KroneckerQuiver`, or `Quiver(n, [[from,to],…])`

Examples

See also: QuiverCompose, QuiverIsAcyclic, Basis