The commutator algebra of a nilpotent matrix and an application to the   theory of commutative Artinian algebras
  We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the results are applied to prove that certain Artinian complete intersections have the strong Lefscehtz property. 
Tadahito Harima and Junzo Watanabe
math.AC