Dihedral homology of commutative algebras Original Research Article

Let A be an associative k-algebra with involution, where k is a commutative ring of characteristic not equal to two. Then the dihedral groups act on the Hochschild complex and, following Loday, a new homological theory, called dihedral homology, can be defined generalizing the notion of cyclic homology defined by Connes. Here we give a model to compute dihedral homology of a commutative algebra over a characteristic zero field. As, for an involutive algebra, we have a decomposition of Hochschild homology into a direct sum of two k-modules: image and skew image Hochschild homologies, we give smoothness criteria in terms of vanishing of some image Hochschild homology groups.