---
tag: 2WWWJMM4AH
kind: statement
role: theorem
name: Skowronski–Weyman theorem
sources:
  - wikipedia: en:42294499@r1312799207
    locator: Semi-invariant of a quiver, section Characterization of representation type through semi-invariant theory > Skowronski–Weyman theorem
    note: adopted
    mention: wikipedia://en/42294499#UXNR
    sections: [Statement]
inventory: [J4E7WE8C2D]
---

## Statement

Let *Q* be a finite connected quiver. The following are equivalent:

1. *Q* is either a Dynkin quiver or a Euclidean quiver.
1. For each dimension vector **d**, the algebra SI(*Q*,**d**) is complete intersection.
1. For each dimension vector **d**, the algebra SI(*Q*,**d**) is either a polynomial algebra or a hypersurface.