MATRADS, BIASSOCIAHEDRA, AND A(infinity)-BIALGEBRAS

作者：Saneblidze Samson^*; Umble Ronald

来源：Homology, Homotopy and Applications, 2011, 13(1): 1-57.

DOI：10.4310/HHA.2011.v13.n1.a1

• A(infinity)-bialgebra
• operad
• matrad
• permutahedron
• biassociahedron

We introduce the notion of a matrad M - {M-n,M-m} whose submodules M-*,M-1 and M-1,M-* are non-Sigma operads. We define the free matrad H 1 generated by a singleton theta(n)(m) in each bidegree (m, n) and realize H-infinity as the cellular chains on a new family of polytopes {KKn,m = KKm,n}, called biassociahedra, of which KKn,1 = KK1,n is the associahedron K-n. We construct the universal enveloping functor from matrads to PROPs and define an A(infinity)-bialgebra as an algebra over H-infinity.

• 出版日期2011