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Homological models for semidirect products of finitely generated Abelian groups

 

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Opened Access Homological models for semidirect products of finitely generated Abelian groups
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Author: Álvarez Solano, Víctor
Frau García, María Dolores
Real Jurado, Pedro
Armario Sampalo, José Andrés
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2012
Published in: Applicable Algebra in Engineering, Communication and Computing, 23 (1), 101-127.
Document type: Article
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, 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).
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URI: http://hdl.handle.net/11441/32916

DOI: http://dx.doi.org/10.1007/s00200-012-0163-y

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