nLab
Koszul algebra

Definition

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.

Revised on February 18, 2012 14:21:54 by Urs Schreiber (89.204.130.11)