论文标题
全组C $^*$ - 代数的提升属性的共同体学障碍
Cohomological obstructions to lifting properties for full group C$^*$-algebras
论文作者
论文摘要
我们基于第二个共同体学组的非逐步播出，开发了一种新方法，以证明具有（相对）属性（t）的可数组的完整c $^*$的提升属性失败。我们得出的是，组的完整c $^*$ - $ \ mathbb z^2 \ rtimes \ text {sl} _2（\ mathbb z）$和$ \ text {sl} _n（\ mathbb z）$，对于$ n \ geq 3 $，没有本地生活（llp）。我们还证明，大型组$γ$与属性（t）的完整C $^*$ - 包括$ \ text {h}^2（γ，\ mathbb r）\ not = 0 $或$ \ not = 0 $或$ \ text {h}^2（γ，γ，\ mathbzγ）更普遍地，我们表明，如果$γ$承认概率度量保留行动，则使用第二$ \ Mathbb r $ $ $ $值同时，这也是如此。最后，我们证明了任何非最终介绍属性（T）组的完整c $^*$ - 失败的代数。
We develop a new method, based on non-vanishing of second cohomology groups, for proving the failure of lifting properties for full C$^*$-algebras of countable groups with (relative) property (T). We derive that the full C$^*$-algebras of the groups $\mathbb Z^2\rtimes\text{SL}_2(\mathbb Z)$ and $\text{SL}_n(\mathbb Z)$, for $n\geq 3$, do not have the local lifting property (LLP). We also prove that the full C$^*$-algebras of a large class of groups $Γ$ with property (T), including those such that $\text{H}^2(Γ,\mathbb R)\not=0$ or $\text{H}^2(Γ,\mathbb ZΓ)\not=0$, do not have the lifting property (LP). More generally, we show that the same holds if $Γ$ admits a probability measure preserving action with non-vanishing second $\mathbb R$-valued cohomology. Finally, we prove that the full C$^*$-algebra of any non-finitely presented property (T) group fails the LP.
