Cyclic Gamma Homology and Gamma Homology for Associative Algebras

Abstract The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes' periodicity sequence becomes almost trivial, because the cyclic version coincides with the ordinary version from homological degree two on. We show that a possible desymmetrized definition of Gamma homology coincides with a shifted version of Hochschild homology and its associated cyclic theory does the same.