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Cup \(i\)-product on the graded algebras with symmetries and Gerstenhaber algebra. (Cup \(i\)-produit sur les algèbres graduées avec symétries et algèbres de Gerstenhaber.) (French. English summary) Zbl 1291.18024
In this work, the author defines the notion of cup \(i\)-products on the graded algebras with symmetries. She proves a nice relation between these cup \(i\)-products and the differential forms of the graded algebras with symmetries. These algebras are a generalization of the noncommutative differential forms algebras which were defined by A. Connes [Publ. Math., Inst. Hautes Étud. Sci. 62, 41–144 (1985; Zbl 0592.46056)]. The author proves that the cohomology of a graded algebra with symmetries is a Gerstenhaber algebra.
18G55 Nonabelian homotopical algebra (MSC2010)
58A10 Differential forms in global analysis
Full Text: DOI
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