Factorization structures with a two-dimensional factor

Autores: Óscar Cortadellas Izquierdo, Javier López Peña, Gabriel Navarro Ortega
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 1, 2010, págs. 1-23
Idioma: inglés
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Resumen
- 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.