论文标题
建设性的证据表明，许多非扭转2-杂种学的组在术中不是稳定的
A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
论文作者
论文摘要
如果从组到一个复杂的统一组的每个函数在点 - 操作员规范拓扑中几乎是乘法的，则离散群在术中是稳定的。从达达拉特（Dadarat）引起的最新结果之后，所有可符合性的群体具有非扭转积分2-杂种学的群体并不稳定，但是证明并没有导致明确的渐近表达式实例，这些例子与真实表示不违反。本文的目的是根据共同体数据给出一个明确的公式，对于一类包含所有有限生成的基团的组的渐近表示，这些组与中央延伸相对应的一类，其中包含所有有限的2-综合学类别，该类别与中间组相对应。该类包括具有非扭转2-综合学的多环类。
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent result due to Dadarlat that all amenable, groups with non-torsion integral 2-cohomology are not matricially stable, but the proof does not lead to explicit examples of asymptotic representations that are not perturbable to genuine representations. The purpose of this paper is to give an explicit formula, in terms of cohomological data, for asymptotic representations that are not perturbable to genuine representations for a class of groups that contains all finitely generated groups with a non-torsion 2-cohomology class that corresponds to a central extension where the middle group is residually finite. This class includes polycyclic groups with non-torsion 2-cohomology.
