The Biderivative and A_∞-bialgebras

2004/06/30 by Samson Saneblidze, Ronald Umble
Mathematics · #math.AT #msc:55P35 #msc:55P99 #msc:52B05

paper · pdf

published as J. Homology, Homotopy and Appl., 7 No. 2 (2005), pp. 161-177. · 15 pages, 5 figures. This final version (3-19-05) features improved graphics and other minor improvements

arxiv created 2005/03/20 · arxiv updated 2009/12/01

Abstract

An A_∞-bialgebra is a DGM H equipped with structurally compatible operations ω^j,i : H^{⊗ i} --> H^{⊗ j} such that (H,ω^1,i) is an A_∞-algebra and (H,ω^j,1) is an A_∞-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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