The Multiplicative Structure on Hochschild Cohomology of a Complete   Intersection
  We determine the product structure on Hochschild cohomology of commutative algebras in low degrees, obtaining the answer in all degrees for complete intersection algebras. As applications, we consider cyclic extension algebras as well as Hochschild and ordinary cohomology of finite abelian groups. 
Ragnar-Olaf Buchweitz and Collin Roberts
math.AC math.AG math.RT