Higher Hochschild homology is not a stable invariant
MetadataShow full item record
The purpose of this thesis is to study the higher Hochschild homology of some rational algebras. We know that for some algebras the higher Hochschild homology is a stable invariant. Studying the homology over the spheres and over the torus, we can deduce that this is not true in the most general sense. We will give a counterexample based on the algebra of the dual numbers over a field of characteristic 0. Moreover we will study the equivariant structure of the iterated Hochschild homology for some particular algebras as a toy model, in order to shed some lights on the limits of the topological version of the Hochschild homology, which plays a key role in the understanding of the chromatic shift of K- theory.