Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective

  • Ronold N. UmbleEmail author
Part of the Progress in Mathematics book series (PM, volume 287)


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.

Associahedron A(n)-algebra A-bialgebra Bialgebradeformation Biderivative Deformation cohomology Matrad Operad Permutahedron 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsMillersville University of PennsylvaniaMillersvilleUSA

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