Abstract
At the 1996 conference honoring Jim Stasheff in the year of his 60th birthday, I initiated the search for A ∞ -bialgebras in a talk entitled “In Search of Higher Homotopy Hopf Algebras.” The idea in that talk was to think of a DG bialgebra as some (unknown) higher homotopy structure with trivial higher order structure and apply a graded version of Gerstenhaber and Schack’s bialgebra deformation theory. Indeed, deformation cohomology, which detects some (but not all) A ∞ -bialgebra structure, motivated the definition given by S. Saneblidze and myself in 2004.
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Umble, R.N. (2011). Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective. In: Cattaneo, A., Giaquinto, A., Xu, P. (eds) Higher Structures in Geometry and Physics. Progress in Mathematics, vol 287. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4735-3_16
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