A positively graded algebra $A$ is called **Koszul** (after Jean-Louis Koszul) if every graded simple object has a projective resolution where the $i$th term is generated in grade $i$. Equivalently, this holds if the internal and homological gradings on the Ext $A^!=\Ext_A(A_0,A_0)$ coincide.

The algebra $(A^!)^{\op}$ is itself Koszul and is called the *Koszul dual* of $A$.

Last revised on February 17, 2015 at 18:02:47. See the history of this page for a list of all contributions to it.