Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective
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Publication:2997026
zbMATH Open1228.13019arXiv0709.3436MaRDI QIDQ2997026
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Publication date: 6 May 2011
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.
Full work available at URL: https://arxiv.org/abs/0709.3436
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