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Search: All articles in the CMB digital archive with keyword building

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1. CMB 2014 (vol 57 pp. 390)

Morita, Jun; Rémy, Bertrand
Simplicity of Some Twin Tree Automorphism Groups with Trivial Commutation Relations
We prove simplicity for incomplete rank 2 Kac-Moody groups over algebraic closures of finite fields with trivial commutation relations between root groups corresponding to prenilpotent pairs. We don't use the (yet unknown) simplicity of the corresponding finitely generated groups (i.e., when the ground field is finite). Nevertheless we use the fact that the latter groups are just infinite (modulo center).

Keywords:Kac-Moody group, twin tree, simplicity, root system, building
Categories:20G44, 20E42, 51E24

2. CMB 2006 (vol 49 pp. 321)

Balser, Andreas
Polygons with Prescribed Gauss Map in Hadamard Spaces and Euclidean Buildings
We show that given a stable weighted configuration on the asymptotic boundary of a locally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration. Moreover, the same result holds for semistable configurations on arbitrary Euclidean buildings.

Keywords:Euclidean buildings, Hadamard spaces, polygons

3. CMB 2001 (vol 44 pp. 385)

Ballantine, Cristina M.
A Hypergraph with Commuting Partial Laplacians
Let $F$ be a totally real number field and let $\GL_{n}$ be the general linear group of rank $n$ over $F$. Let $\mathfrak{p}$ be a prime ideal of $F$ and $F_{\mathfrak{p}}$ the completion of $F$ with respect to the valuation induced by $\mathfrak{p}$. We will consider a finite quotient of the affine building of the group $\GL_{n}$ over the field $F_{\mathfrak{p}}$. We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph.

Keywords:Hecke operators, buildings
Categories:11F25, 20F32

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