DG余代数的循环同调和一个Kuenneth公式
Cyclic Homology of DG Coalgebras and a Kuenneth Formula
摘要：
本文将循环同调函子，特别是周期循环同调推广到微分分次余代数范畴.我们的部分动机是由A. Connes开创的代数循环同调中的积和上积问题。作为一个应用，我们展示了如何从同调代数和代数拓扑学中的经典shuffle映射出发，建立周期和负循环同调中的乘积和上积理论，该映射被Husemoller，Moore和Stasheff解释为DG余代数的态射.其中一个关键的成分是由于Cuntz和Quillen的X复合体的想法，适当地扩展到DG colagebras。
英文摘要：
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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