Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective
Abstract
The search for higher homotopy Hopf algebras (known today as A_\infty-bialgebras) began in 1996 during a conference at Vassar College honoring Jim Stasheff in the year of his 60th birthday. In a talk entitled "In Search of Higher Homotopy Hopf Algebras", I indicated that a DG Hopf algebra could be thought of as some (unknown) higher homotopy structure with trivial higher order structure and deformed using a graded version of Gerstenhaber and Schack's bialgebra deformation theory. In retrospect, the bi(co)module structure encoded in Gerstenhaber and Schack's differential defining deformation cohomology detects some (but not all) of the A_infty-bialgebra structure relations. Nevertheless, this motivated the discovery of A_infty-bialgebras by S. Saneblidze and myself in 2005.
Keywords
Cite
@article{arxiv.0709.3436,
title = {Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective},
author = {Ronald N. Umble},
journal= {arXiv preprint arXiv:0709.3436},
year = {2010}
}
Comments
17 pages; 7 figures; this revision cleans up the bibliography and replaces the term "matrahedron" with "biassociahedron"