Dihedral homology of commutative algebras. (English) Zbl 0872.13008
The authors use the techniques developed by D. Burghelea and 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 A. R. Rodicio [Comment. Math. Helv. 65, No. 3, 474-477 (1990; Zbl 0726.13008)] is given.
Reviewer: M.Golasiński (Toruń)
MSC:
| 13D03 | (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
| 18G60 | Other (co)homology theories (MSC2010) |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
Keywords:
dihedral homology; differential graded algebra; involutive graded algebra; polynomial algebra; Hochschild homologyReferences:
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