Homogeneous algebras

Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree 1 with homogeneous relations of degree N. Such algebras are referred to as homogeneous algebras of degree N. In particular, it is shown that the Koszul complexes of quadratic algebras generalize as N-complexes for homogeneous algebras of degree N.