Homology, Homotopy and Applications

The biderivative and $A\sb \infty$-bialgebras

Samson Saneblidze and Ronald Umble

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Abstract

An $A_{\infty }$-bialgebra is a DGM $H$ equipped with structurally compatible operations $\left\{ \omega ^{j,i}:H^{\otimes i}\rightarrow H^{\otimes j}\right\} $ such that $\left( H,\omega ^{1,i}\right) $ is an $% A_{\infty }$-algebra and $\left( H,\omega ^{j,1}\right) $ is an $A_{\infty }$% -coalgebra. Structural compatibility is controlled by the biderivative operator $Bd$, defined in terms of two kinds of cup products on certain cochain algebras of pemutahedra over the universal PROP $U=End\left(TH\right)$.

Article information

Source
Homology Homotopy Appl., Volume 7, Number 2 (2005), 161-177.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139839380

Mathematical Reviews number (MathSciNet)
MR2156313

Zentralblatt MATH identifier
1088.55008

Subjects
Primary: 55P35: Loop spaces
Secondary: 18D50: Operads [See also 55P48]

Citation

Saneblidze, Samson; Umble, Ronald. The biderivative and $A\sb \infty$-bialgebras. Homology Homotopy Appl. 7 (2005), no. 2, 161--177. https://projecteuclid.org/euclid.hha/1139839380


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