PathAlgebra

The path algebra $kQ$ of a quiver: basis QuiverPath, product concatenation, finite-dimensional exactly when the quiver is acyclic.

PathAlgebra(quiver)$kQ$, the algebra of directed paths in the quiver

Typed signatures

Type	Package	Applies
(expression<LinearQuiver> | expression<Quiver> | symbol) -> path_algebra	quiver	always

Domain: Path algebras

Examples

Basic #

$\binom{5}{2}$ paths

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{PathAlgebra}(\mathrm{LinearQuiver}(4)))$Out$10$

Two parallel arrows: $2+2$ vertex and arrow paths

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{PathAlgebra}(\mathrm{Quiver}(2, \bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack1, 2\bigr\rbrack\bigr\rbrack)))$Out$4$

About

Examples	2

See also: Quiver, QuiverIsAcyclic, QuiverPath