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The Biderivative and A_\infty-bialgebras

Samson Saneblidze·Ronald Umble
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Abstract

An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {ω^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,ω^{1,i}) is an A_\infty-algebra and (H,ω^{j,1}) is an A_\infty-coalgebra. Structural compatibility is controlled by the biderivative operator Bd, defined in terms of two kinds of cup products on certain cochain algebras of pemutahedra over the universal PROP U = End(TH).

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Samson Saneblidze, Ronald Umble. 2005-03-20. The Biderivative and A_\infty-bialgebras. https://arxiv.org/abs/math/0406270

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