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 ⊕Mn,1 and ⊕M1,m 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, among w...
متن کامل. A T ] 5 J an 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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