The Cartan determinant conjecture for quiver algebras. The Cartan determinant conjecture states that every finite dimensional algebra of finite global dimension has the property that the determinant of its Cartan matrix is equal to one. For quiver algebras the problem would reduce to a linear algebra problem concerned with graphs understandable to any student with knowledge of basic linear algebra. And a proof for quiver algebras would provide a proof of the general conjecture over algebraically closed fields. The Cartan matrix of a finite dimensional quiver algebra is defined as the matrix having entries $c_{i,j}:=$dimension of the vector space $e_i A e_j$, which is the space generated by all paths from $i$ to $j$ in the quiver.