Koszul calculus for N-homogeneous algebras
  We extend the Koszul calculus defined on quadratic algebras by Berger, Lambre and Solotar, to N-homogeneous algebras. When N>2, the Koszul cup and cap products are defined by specific expressions, and they are compatible with the Koszul differentials, providing associative products on (co)homology classes. The N-Koszul calculus is calculated for the truncated polynomial algebras. 
Roland Berger
math.RA math.RT