Cyclic Homology of DG Coalgebras and a Kuenneth Formula

Details Cyclic Homology of DG Coalgebras and a Kuenneth Formula Cyclic Homology of DG Coalgebras and a Kuenneth Formula

1998-06-19

arxiv.org/abs/math/9806110v1

Mathematics

Quantum Algebra

Scientific paper

In this note we extend the cyclic homology functor, and in particular the periodic cyclic homology, to the category of DG (= differential graded) coalgebras. We are partly motivated by the question of products and coproducts in the cyclic homology of algebras, pioneered by A.Connes. As an application we show how one can start from the classical shuffle map in homological algebra and algebraic topology, interpreted by Husemoller, Moore and Stasheff as a morphism of DG coalgebras, and build a theory of products and coproducts in periodic and negative cyclic homology. One of the key ingredients is the idea of X-complex due to Cuntz and Quillen, suitably extended to DG colagebras.

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