Capítulo de Libro
Comparison maps for relatively free resolutions
Autor/es | Álvarez Solano, Víctor
Armario Sampalo, José Andrés Frau García, María Dolores Real Jurado, Pedro |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2006 |
Fecha de depósito | 2015-12-09 |
Publicado en |
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Resumen | Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides ... Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) 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=1 X 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,μ X ) is shown to be a commutative DGA-algebra with the product μ X =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. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Comparison maps.pdf | 537.6Kb | [PDF] | Ver/ | |