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Graded algebras with symmetries. (Algèbres graduées avec symétries.) (French) Zbl 1238.16008
Author’s summary: We define the notion of “graded algebra with symmetries”. This notion is a generalization of the extended differential forms. We prove that for a graded algebra with symmetries \(T\), we associate a subalgebra \(\Omega^*\) which generalizes the noncommutative differential forms. Using this algebra \(\Omega^*\), we can define the Hochschild and cyclic homologies, cup \(i\)-products and the Steenrod squares.

16E45 Differential graded algebras and applications (associative algebraic aspects)
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
55S10 Steenrod algebra
58A10 Differential forms in global analysis
18G55 Nonabelian homotopical algebra (MSC2010)
Full Text: DOI
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