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Journal of the London Mathematical Society Advance Access published online on November 3, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp055
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© 2009 London Mathematical Society

Factorization structures with a two-dimensional factor

Óscar Cortadellas

Department of Algebra
University of Granada
Avda. Fuentenueva s/n. E-18071
Granada
Spain
ocortad@ugr.es

Javier López Peña

Mathematics Research Centre
Queen Mary University of London
Mile End Road
London
E1 4NS
United Kingdom

Gabriel Navarro

Department of Computer Sciences and AI
University of Granada
C/ El Greco s/n. E-51002
Ceuta
Spain
gnavarro@ugr.es

We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model relies on the classification of factorization structures with a two-dimensional factor. In the present paper, main properties of this particular kind of structure are determined, and we present a complete description of quantum duplicates of finite set algebras. As an application, we obtain a classification (up to isomorphism) of all the algebras of dimension 4 (over an arbitrary field) that can be factorized as a product of two factors.

2000 Mathematics Subject Classification 16S35, 16G20, 16W35.

This research was supported by MTM2007-66666, FQM-1889 and FQM-266. The second author was supported by Max-Planck Institut für Mathematik in Bonn and the EU Marie-Curie fellowship PIEF-GA-2008-221519 at Queen Mary University of London.

Received September 17, 2008; revised July 13, 2009;
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