矩阵、双结合面体与A_{\infty} -双代数
Matrads, Biassociahedra and A_{\infty}-Bialgebras
摘要：
我们引入矩阵M = { M_{n,m} }的概念，它的子模M_{*,1}和M_{1,*}是非Sigma运算.我们定义了每个二度（m，n）上的单点生成的自由矩阵H_{\infty}，并将H_{\infty}实现为双缔合多面体KK_{n,m} = KK_{m,n}上的胞元链，其中KK_{n,1} = KK_{1,n}是缔合多面体K_{n} .我们构造了从矩阵到PROP的泛包络函子，定义了一个A_{\infty} -双代数为H_{\infty}上的代数.
英文摘要：
We introduce the notion of a matrad M = {M_{n,m}} whose submodules M_{*,1} and M_{1,*} are non-Sigma operads. We define the free matrad H_{\infty} generated by a singleton in each bidegree (m,n) and realize H_{\infty} as the cellular chains on biassociahedra KK_{n,m} = KK_{m,n}, of which KK_{n,1} = KK_{1,n} is the associahedron K_{n}. We construct the universal enveloping functor from matrads to PROPs and define an A_{\infty}-bialgebra as an algebra over H_{\infty}.
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