Combinatorial operad actions on cochains
Combinatorial operad actions on cochains
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Cochains 上的组合操作
DOI：
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发表时间：
2001
影响因子：
0.8
通讯作者：
B. Fresse
中科院分区：
文献类型：
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作者：
C. Berger;B. Fresse
一个经典的E-无穷操作数是由对称群的棒构造形成的。M. Barratt和P. Eccles在单纯集的上下文中，为了有一个类似的Milnor FK-构造无限循环空间。证明了单纯集的正规上链复形上的结合代数结构推广到Barratt-Eccles运算上的代数结构。我们还证明了Barratt-Eccles算子上的微分分次代数形成一个闭模型范畴。结合代数的正规化Hochschild上链复形也有类似的结果。更确切地说，Hochschild上链复形是由Barratt-Eccles操作数的一个子操作数作用的，它等价于经典的小平方操作数。
A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial sets in order to have an analogue of the Milnor FK-construction for infinite loop spaces. The purpose of this paper is to prove that the associative algebra structure on the normalized cochain complex of a simplicial set extends to the structure of an algebra over the Barratt–Eccles operad. We also prove that differential graded algebras over the Barratt–Eccles operad form a closed model category. Similar results hold for the normalized Hochschild cochain complex of an associative algebra. More precisely, the Hochschild cochain complex is acted on by a suboperad of the Barratt–Eccles operad which is equivalent to the classical little squares operad.