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 { \sl 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.
Categories: math.QA hep-th math-ph math.KT math.MP math.RA