Homological models for semidirect products of finitely generated Abelian groups

Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, B¯¯¯¯(ZZ[G]) , to a much smaller DGA-module hG. Such a contraction is called a hom...

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Detalles Bibliográficos
Autores: Álvarez Solano, Víctor, Frau García, María Dolores, Real Jurado, Pedro, Armario Sampalo, José Andrés
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32916
Acceso en línea:http://hdl.handle.net/11441/32916
https://doi.org/10.1007/s00200-012-0163-y
Access Level:acceso abierto
Palabra clave:Semidirect product of groups
Homological model
Contraction
Homological perturbation theory
Descripción
Sumario:Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, B¯¯¯¯(ZZ[G]) , to a much smaller DGA-module hG. Such a contraction is called a homological model for G and is used as the input datum in the methods described in Álvarez et al. (J Symb Comput 44:558–570, 2009; 2012) for calculating a generating set for representative 2-cocycles and n-cocycles over G, respectively. These computations have led to the finding of new cocyclic Hadamard matrices (Álvarez et al. in 2006).