##  [Path Algebra](/path-algebra) 

  ##  [Path Algebra](https://algebra.quantumdictionary.io/path-algebra-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An associative algebra whose basis consists of all directed paths in a quiver (directed graph), with multiplication given by concatenation of paths when the target of the first equals the source of the second and defined to be zero otherwise, and with vertex idempotents corresponding to trivial paths.