| Título: | Classification of finitely generated lattice-ordered groups with order-unit |
| Autores: |
Manuela Busaniche; IMAL-CONICET-UNL Leonardo Cabrer D. Mundici |
| Fecha: | 2009-04-08 |
| Publicador: | Centro Internacional de Métodos Numéricos en Ingeniería |
| Fuente: |
Ver documento |
| Tipo: |
Articles |
| Tema: | No aplica |
| Descripción: | A unital $\ell$-group $(G,u)$ is an abelian group $G$ equipped with a translation-invariant lattice-order and a distinguished element $u$, called order-unit, whose positive integer multiples eventually dominate each element of $G$. We classify finitely generated unital $\ell$-groups by sequences $\mathcal W = (W_{0},W_{1},\ldots)$ of weighted abstract simplicial complexes, where $W_{t+1}$ is obtained from $W_{t}$ either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of $W_{t}$. A simple criterion is given to recognize when two such sequences classify isomorphic unital $\ell$-groups. Many properties of the unital $\ell$-group $(G,u)$ can be directly read off from its associated sequence: for instance, the properties of being totally ordered, archimedean, finitely presented, simplicial, free. |
| Idioma: | Inglés |
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