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Homological models for semidirect products of finitely generated Abelian groups

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Abstract

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, \({\overline{B}(\mathsf{\textstyle Z\kern-0.4em Z}[G])}\) , 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).

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Authors and Affiliations

  1. Departamento de matemática Aplicada I. ETSI Informática, Universidad de Sevilla, Avda Reina Mercedes s/n, 41012, Sevilla, Spain

    Víctor Álvarez, José Andrés Armario, María Dolores Frau & Pedro Real

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  1. Víctor Álvarez
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  2. José Andrés Armario
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  3. María Dolores Frau
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  4. Pedro Real
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Correspondence to José Andrés Armario.

Additional information

V. Álvarez, J. A. Armario and M.D Frau have been partially supported by Junta de Andalucía, projects: FQM016 and P07-FQM-02980, and by MICINN (Spain) and FEDER (European Union), project: MTM2008-06578. P. Real has been partially supported by Junta de Andalucía, projects: FQM296 and P06-TIC-02268, And by MICINN (Spain) and FEDER (European Union), project: MTM2009-12716.

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Álvarez, V., Armario, J.A., Frau, M.D. et al. Homological models for semidirect products of finitely generated Abelian groups. AAECC 23, 101–127 (2012). https://doi.org/10.1007/s00200-012-0163-y

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  • DOI: https://doi.org/10.1007/s00200-012-0163-y

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