The Biderivative and A_\infty-bialgebras
Algebraic Topology
2007-05-23 v7
Abstract
An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {\omega^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,\omega^{1,i}) is an A_\infty-algebra and (H,\omega^{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).
Cite
@article{arxiv.math/0406270,
title = {The Biderivative and A_\infty-bialgebras},
author = {Samson Saneblidze and Ronald Umble},
journal= {arXiv preprint arXiv:math/0406270},
year = {2007}
}
Comments
15 pages, 5 figures. This final version (3-19-05) features improved graphics and other minor improvements