nLab Koszul algebra


A positively graded algebra AA is called Koszul (after Jean-Louis Koszul) if every graded simple object has a projective resolution where the iith term is generated in grade ii. Equivalently, this holds if the internal and homological gradings on the Ext A !=Ext A(A 0,A 0)A^!=\Ext_A(A_0,A_0) coincide.

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

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