Homotopy Operations for Simplicial Commutative Algebras
نویسنده
چکیده
The indicated operation algebra is studied by methods dual to the usual ones for studying the Steenrod algebra. In particular, the operations are constructed using higher symmetries of the shuffle map and their "Adem relations" are computed using the transfer map in the cohomology of symmetric groups.
منابع مشابه
Cartan Operations for Simplicial Algebras over an Operad
By a result of H. Cartan (cf. 5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of Cartan operations in the context of simplicial algebras over an operad.
متن کاملNilpotency in the Homotopy of Simplicial Commutative Algebras
In this paper, we continue a study of simplicial commutative algebras with finite André-Quillen homology, that was begun in [19]. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of the main theorem in [19]. In particular, we replace the finiteness condition on homotopy with a weaker condition expressed in terms of nilpotency for the...
متن کاملOn the Homotopy of Simplicial Algebras over an Operad
According to a result of H. Cartan (cf. [5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of such operations in the context of simplicial algebras over an operad. To be precise, we work over a fixed field F, and we consider operads in the category of F-modules. An operad is an algebr...
متن کاملCharacterizing Simplicial Commutative Algebras with Vanishing André-Quillen Homology
The use of homological and homotopical devices, such as Tor and AndréQuillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of ...
متن کاملRelations in the Homotopy of Simplicial Abelian Hopf Algebras
In this paper, we analyze the structure possessed by the homotopy groups of a simplicial abelian Hopf algebra over the field F2. Specifically, we review the higher-order structure that the homotopy groups of a simplicial commutative algebra and simplicial cocommutative coalgebra possess. We then demonstrate how these structures interact under the added conditions present in a Hopf algebra. Intr...
متن کامل