Comparison maps for relatively free resolutions
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...
| Autores: | , , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/31615 |
| Acceso en línea: | http://hdl.handle.net/11441/31615 https://doi.org/10.1007/11870814_1 |
| Access Level: | acceso abierto |
| Palabra clave: | Symbolic and Algebraic Manipulation Programming Techniques Discrete Mathematics in Computer Science Algorithm Analysis and Problem Complexity Math Applications in Computer Science Algorithms |
| Sumario: | 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. |
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