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Higher Homotopy Hopf Algebras Found: A Ten Year Retrospective

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Book cover Higher Structures in Geometry and Physics

Part of the book series: Progress in Mathematics ((PM,volume 287))

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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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Authors and Affiliations

  1. Department of Mathematics, Millersville University of Pennsylvania, Millersville, PA, 17551, USA

    Ronold N. Umble

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  1. Ronold N. Umble
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Correspondence to Ronold N. Umble .

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Editors and Affiliations

  1. Universität Zürich, Institut für Mathematik, Winterthurerstr. 190, Zürich, CH-8057, Switzerland

    Alberto S. Cattaneo

  2. Loyola University, Chicago, Department of Mathematics, Chicago, 60626, Illinois, USA

    Anthony Giaquinto

  3. Pennsylvania State University, Department of Mathematics, Eberly College of Science, University Park, 16802, Pennsylvania, USA

    Ping Xu

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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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