Dihedral homology of commutative algebras (Q1916402)

The authors use the techniques developed by \textit{D. Burghelea} and \textit{M. Vigué Poirrier} [in: Algebraic topology, rational homotopy, Proc. Conf. Louvain-la-Neuve 1986, Lect. Notes Math. 1318, 51-72 (1988; Zbl 0666.13007)] to study \(\mathbb{Z}_2\)-equivariant Hochschild and dihedral homology of an involutive algebra over a characteristic zero field. A sufficient and necessary condition for an involutive graded algebra to be a polynomial algebra, in terms of vanishing of these homology groups is shown. Then, a positive answer to a refinement of a conjecture by \textit{A. R. Rodicio} [Comment. Math. Helv. 65, No. 3, 474-477 (1990; Zbl 0726.13008)] is given.