منابع مشابه
Boundary Operator Algebras for Free Uniform Tree Lattices
Let X be a finite connected graph, each of whose vertices has degree at least three. The fundamental group Γ of X is a free group and acts on the universal covering tree ∆ and on its boundary ∂∆, endowed with a natural topology and Borel measure. The crossed product C∗-algebra C(∂∆)⋊Γ depends only on the rank of Γ and is a Cuntz-Krieger algebra whose structure is explicitly determined. The cros...
متن کاملCongruence Lattices of Uniform Lattices
A lattice L is uniform, if for any congruence Θ of L, any two congruence classes A and B of Θ are of the same size, that is, |A| = |B| holds. A classical result of R. P. Dilworth represents a finite distributive lattice D as the congruence lattice of a finite lattice L. We show that this L can be constructed as a finite uniform lattice.
متن کاملNon-minimal Tree Actions and the Existence of Non-uniform Tree Lattices
A uniform tree is a tree that covers a finite connected graph. Let X be any locally finite tree. Then G = Aut(X) is a locally compact group. We show that if X is uniform, and if the restriction of G to the unique minimal G-invariant subtree X0 ⊆ X is not discrete then G contains non-uniform lattices; that is, discrete subgroups Γ for which Γ\G is not compact, yet carries a finite G-invariant me...
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We study the Hard Core Model on the graphs G obtained from Archimedean tilings i.e. configurations in {0,1} with the nearest neighbor 1’s forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cel...
متن کاملLattices on Non-uniform Trees
Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup Γ such that the quotient graph of groups Γ\\X is infinite but has finite covolume, then G contains a non-uniform lattice, that is, a discrete subgroup Λ such that Λ\G is not compact, yet has a finite G-invariant measure. 0. Notatio...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1990
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-1990-1065928-2