%0 Journal Article
%T Factorization structures with a 2-dimensional factor
%A ¨®scar Cortadellas
%A Javier L¨®pez PeŁża
%A Gabriel Navarro
%J Mathematics
%D 2008
%I arXiv
%R 10.1112/jlms/jdp055
%X 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 structures 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.
%U http://arxiv.org/abs/0807.1826v2