Higher Homotpy Hopf Algebra Found: a Ten Year Retrospective
نویسنده
چکیده
The search for higher homotopy Hopf algebras (known today as A∞-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∞-bialgebra structure relations. Nevertheless, this motivated the discovery of A∞-bialgebras by S. Saneblidze and myself in 2005. To Murray Gerstenhaber and Jim Stasheff
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Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
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