Daniele Mundici
Measure theory in the geometry of $GL(n,\mathbb Z) \ltimes \mathbb Z^{n}$.
Mon, 02/07/2011 - 16:01 — SomNambulAuthors: Daniele Mundici
Subjects: General Topology
AbstractThe $n$-dimensional affine group over the integers is the group $\mathcal
G_n$ of all affinities on $\mathbb R^{n}$ which leave the lattice $ \mathbb
Z^{n}$ invariant. $\mathcal G_n$ yields a geometry in the classical sense of
the Erlangen Program.Finitely presented lattice-ordered abelian groups with order-unit.
Wed, 06/23/2010 - 15:01 — SomNambulAuthors: Leonardo Cabrer, Daniele Mundici
Subjects: Group Theory
AbstractLet $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian
group''). Baker and Beynon proved that $G$ is finitely presented iff it is
finitely generated and projective. In the category $\mathcal U$ of {\it unital}
$\ell$-groups---those $\ell$-groups having a distinguished order-unit
$u$---only the $(\Leftarrow)$-direction holds in general. Morphisms in
$\mathcal U$ are {\it unital $\ell$-homomorphisms,} i.e., hom\-o\-mor\-phisms
that preserve the order-unit and the lattice structure.Classification of finitely generated lattice-ordered abelian groups with order-unit.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: Manuela Busaniche, Leonardo Cabrer, Daniele Mundici
Subjects: Group Theory
AbstractA 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
$\mathcal W = (W_{0},W_{1},...)$ 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 $W_{t}$.- Read more
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