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Homological models for semidirect products of finitely generated Abelian groups

Victor Alvarez Solano
Organization: University of Seville (Spain)
Department: Matematica Aplicada I
José Andrés Armario
María Dolores Frau
Pedro Real
Journal / Anthology

Applicable Algebra in Engineering Communication and Computing
Year: 2012
Volume: 23
Issue: 1-2
Page range: 101-127

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).

*Mathematics > Algebra

Semidirect product of groups, Homological model, Contraction, Homological perturbation theory