The bar construction of an algebra as an E-infinite Hopf algebra

Details The bar construction of an algebra as an E-infinite Hopf algebra The bar construction of an algebra as an E-infinite Hopf algebra

2003-03-03

arxiv.org/abs/math/0303027v2

Mathematics

Algebraic Topology

6 pages. Minor changes in the revised version

Scientific paper

We prove that the bar construction of an $E_\infty$ algebra forms an
$E_\infty$ algebra. To be more precise, we provide the bar construction of an
algebra over the surjection operad with the structure of a Hopf algebra over
the Barratt-Eccles operad. (The surjection operad and the Barratt-Eccles operad
are classical $E_\infty$ operads.)

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