无限双曲Kazhdan群的16相关表示

L’Enseignement Mathématique Pub Date : 2017-08-31 DOI:10.4171/LEM/64-3/4-2

P. Caprace

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引用次数: 9

摘要

我们给出了一个无限双曲Kazhdan群的显式表示，该群具有$4$生成子和$16$关联子，其长度不超过$73$。该群在类型为$(3,4,4)$的双曲三角形构造上恰当而紧密地起作用。我们还指出了构造的一种变化，得到了$\tilde A_2$-结构中允许任意素数幂阶的非desarguesian残数的格的例子。

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A sixteen-relator presentation of an infinite hyperbolic Kazhdan group

We provide an explicit presentation of an infinite hyperbolic Kazhdan group with $4$ generators and $16$ relators of length at most $73$. That group acts properly and cocompactly on a hyperbolic triangle building of type $(3,4,4)$. We also point out a variation of the construction that yields examples of lattices in $\tilde A_2$-buildings admitting non-Desarguesian residues of arbitrary prime power order.

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L’Enseignement Mathématique

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