. A T ] 5 J an 2 00 6 MATRONS , A ∞ - BIALGEBRAS AND THE POLYTOPES KK
نویسنده
چکیده
We introduce the notion of a matron M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n} , of which KKn,0 = KK0,n is the Stasheff associahedron Kn+1.
منابع مشابه
1 F eb 2 00 6 MATRONS , A ∞ - BIALGEBRAS AND THE POLYTOPES KK
We introduce the notion of a matron M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...
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We introduce the notion of a matron M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...
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We introduce the notion of a matrad M = {Mn,m} whose submodules M∗,1 and M1,∗ are non-Σ operads. We construct a functor from PROP to matrads and its inverse, the universal enveloping functor. We define the free matrad H∞, generated by a singleton in each bidegree (m, n) 6= (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes {KKn,m = KKm,n}...
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A general A∞-infinity bialgebra is a DG module (H, d) equipped with a family of structurally compatible operations ωj,i : H ⊗i → H,where i, j ≥ 1 and i+ j ≥ 3 (see [6]). In special A∞-bialgebras, ωj,i = 0 whenever i, j ≥ 2, and the remaining operationsmi = ω1,i and ∆j = ωj,1 define the underlying A∞-(co)algebra substructure. Thus special A∞-bialgebras have the form (H, d,mi,∆j)i,j≥2 subject to ...
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