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Structure Relations in Special A_\infty-bialgebras
Ronald Umble
We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras a…
The Biderivative and A_\infty-bialgebras
Samson Saneblidze, Ronald Umble
An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {ω^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,ω^{1,i}) is an A_\infty-algebra and (H,ω^…
Diagonals on the Permutahedra, Multiplihedra and Associahedra
Samson Saneblidze, Ronald Umble
We construct an explicit diagonal Δ_P on the permutahedra P. Related diagonals on the multiplihedra J and the associahedra K are induced by Tonks' projection P --> K and its factor…
The Deformation Complex For DG Hopf Algebras
Ronald Umble
Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of…
A Diagonal on the Associahedra
Samson Saneblidze, Ronald Umble
Let C_*(K) denote the cellular chains on the Stasheff associahedra. We construct an explicit combinatorial diagonal Δ: C_*(K) --> C_*(K) \otimes C_*(K); consequently, we obtain an…