Plus-construction for algebras over an operad, cyclic and Hochschild homologies up to homotopy

Details Plus-construction for algebras over an operad, cyclic and Hochschild homologies up to homotopy Plus-construction for algebras over an operad, cyclic and Hochschild homologies up to homotopy

2003-01-13

arxiv.org/abs/math/0301130v2

Mathematics

Algebraic Topology

Scientific paper

In this paper we apply homotopical localization to the framework of differential graded algebras over an operad. We get plus construction by performing nullification with respect to an universal acyclic algebra. This plus construction for Lie and Leibniz algebras up to homotopy yields two new homology theories for associative algebras. They are closely related to cyclic and Hochschild homologies. We also compute their first homology groups.

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