Hochschild (co)homology of two families of complete intersections

Abstract

The thesis presents the original results on a description of the ring structure in terms of generators and relations of the Hochschild cohomology of the two families of complete intersections: the square-free monomial complete intersections and the numerical semigroup algebras of embedding dimension two. In particular, we use the alternative resolution given by Jorge Guccione and Juan Guccione to describe the Hochschild cohomology. Then we describe the Hochschild cohomology modules via sub-complexes of the Hochschild complex which reduces the computations into smaller and simpler complexes. In the next stage, the cup product is described in terms of the Yoneda product. For more details, we provide an explicit formula of the multiplication on these module structures. Finally, we give a description of the ring structures of the algebras in terms of generators and relations and computed the Hilbert series of these algebras. Based on the ideas for the cohomology version, we give some conjectures on the ring structure of the Hochschild homology of the square-free monomial complete intersections.