论文标题
强财产（t），弱舒适性和$ \ ell^p $ - $ \ tilde {a} _2 $ -buildings in $ \ tilde
Strong Property (T), weak amenability and $\ell^p$-cohomology in $\tilde{A}_2$-buildings
论文作者
论文摘要
我们证明，在$ \ tilde {a} _2 $ -buildings满足Lafforgue的强大属性（T）上，COCOCOCACT（更普遍地：未发生的）晶格，因此显示了与本地领域的代数群体无关的第一个示例。我们的方法还给出了进一步的结果。首先，我们证明了$ \ tilde {a} _2 $ - 建筑物的第一个$ \ ell^p $ - 对任何有限$ p $的构建消失。其次，我们表明，$ p $的非交换性$ l^p $ - 空间不在$ [\ frac 4 3,4] $中，而与$ \ tilde {a} _2 _2 $ - lattice相关的$ c^*$ - 代数不具有操作员空间近似属性，因此，lattice note lattice note note note note note note lateby neve neve noce noce noce nemeby amen amen emnemen amen emennemennemennemennemennemennemennemennemennemennemennemennemennemennemennemenneN。
We prove that cocompact (and more generally: undistorted) lattices on $\tilde{A}_2$-buildings satisfy Lafforgue's strong property (T), thus exhibiting the first examples that are not related to algebraic groups over local fields. Our methods also give two further results. First, we show that the first $\ell^p$-cohomology of an $\tilde{A}_2$-building vanishes for any finite $p$. Second, we show that the non-commutative $L^p$-space for $p$ not in $[\frac 4 3,4]$ and the reduced $C^*$-algebra associated to an $\tilde{A}_2$-lattice do not have the operator space approximation property and, consequently, that the lattice is not weakly amenable.
