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On PMinimal Homological Models of Twisted Tensor Products of Elementary Complexes Localised over a Prime
"... In this paper, working over Z (p) and using algebra perturbation results from [18], pminimal homological models of twisted tensor products (TTPs) of Cartan 's elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological m ..."
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Cited by 4 (3 self)
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In this paper, working over Z (p) and using algebra perturbation results from [18], pminimal homological models of twisted tensor products (TTPs) of Cartan 's elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable pminimal TTP of length # (# 2) of exterior and divided power algebras is a tensor product of kindecomposable (k #) pminimal TTPs of exterior and divided power algebras.
Homological Perturbation Theory And Computability Of Hochschild And Cyclic Homologies Of Cdgas
, 1997
"... . We establish an algorithm computing the homology of commutative dierential graded algebras (briey, CDGAs). The main tool in this approach is given by the Homological Perturbation Theory particularized for the algebra category (see [21]). Taking into account these results, we develop and rene some ..."
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Cited by 3 (1 self)
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. We establish an algorithm computing the homology of commutative dierential graded algebras (briey, CDGAs). The main tool in this approach is given by the Homological Perturbation Theory particularized for the algebra category (see [21]). Taking into account these results, we develop and rene some methods already known about the computation of the Hochschild and cyclic homologies of CDGAs. In the last section of the paper, we analyze the plocal homology of the iterated bar construction of a CDGA (p prime). 1. Introduction. The description of eÆcient algorithms of homological computation might be considered as a very important question in Homological Algebra, in order to use those processes mainly in the resolution of problems on algebraic topology; but this subject also inuence directly on the development of non so closedareas as Cohomological Physics (in this sense, we nd useful references in [12], [24], [25]) and Secondary Calculus ([14], [27], [28]). Working in the context ...
Comparison maps for relatively free resolutions ⋆
"... Abstract. Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGAalgebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives ..."
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Abstract. Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGAalgebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f: B(A) → X and g: X → B(A) termed comparison maps. In case that fg = 1X and A is connected, we show that X is endowed a A∞tensor product structure. In case that A is in addition commutative then (X, µX) is shown to be a commutative DGAalgebra with the product µX = f ∗ (g ⊗ g) ( ∗ is the shuffle product in B(A)). Furthermore, f and g are algebra maps. We give an example in order to illustrate the main results of this paper. 1
Cartan’s contructions and the twisted EilenbergZilber theorem 1
"... Let G ×τ G ′ be the principal twisted Cartesian product with fibre G, base G and twisting function τ: G′ ∗ → G∗−1 where G and G ′ are simplicial groups as well as G×τG′; and CN(G)⊗t CN(G′) be the twisted tensor product associated to CN(G×τ G′) by the twisted EilenbergZilber theorem. Here we prove ..."
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Let G ×τ G ′ be the principal twisted Cartesian product with fibre G, base G and twisting function τ: G′ ∗ → G∗−1 where G and G ′ are simplicial groups as well as G×τG′; and CN(G)⊗t CN(G′) be the twisted tensor product associated to CN(G×τ G′) by the twisted EilenbergZilber theorem. Here we prove that the pair (CN(G) ⊗t CN(G′), µ) is a multiplicative Cartan’s construction where µ is the standard product on CN(G)⊗ CN(G′). Furthermore, assuming that a contraction from CN(G′) to HG ′ exists and using techniques from homological perturbation theory, we extend the former result to other “twisted ” tensor products of the form CN(G)⊗HG′.