双导数与A_ \infty -双代数
The Biderivative and A_\infty-bialgebras
摘要：
A_ \infty -双代数是具有结构相容运算{ω^{j，i}的DGMH：H^{ \otimes i} --> H^{ \otimes j}}使得（H，ω^{1，i}）是A_ \infty -代数，（H，ω^{j，1}）是A_ \infty -余代数.结构相容性由双导数算子Bd控制，Bd定义为泛PROP U = End（TH）上半多面体的上链代数上的两种上积.
英文摘要：
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^{j,1}) 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(TH).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
