关于连续变形自由群因子的一些结果
Some results on continuous deformed free group factors
摘要：
我们构造了一个与对称函数$Q:U\times U \to (-1,1)$相关联的Fock空间，其中$U$是$\mathbb R^j$的非空开子集，对于某些$j$。也就是说，我们将有算子值分布$a(x)$和$a^+(y)$满足$a(x)a^+(y)-Q(x,y)a^+(y)a(x)=δ(x-y)$。类似于Bozejko和Speicher的$q_{ij}$ -Fock空间，我们有场算符作为产生算符和湮灭算符之和。这些算子生成一个类似于自由群因子的冯诺依曼代数，我们将证明它们是不具有性质$Γ$的因子。这是向我们指出，由一个匿名裁判，这是一个特殊情况下的定理Krolak。
英文摘要：
We construct a Fock space associated to a symmetric function $Q:U\times U \to (-1,1)$, where $U$ is a nonempty open subset of $\mathbb R^j$ for some $j$. Namely, we will have operator-valued distributions $a(x)$ and $a^+(y)$ satisfying $a(x)a^+(y)-Q(x,y)a^+(y)a(x)=δ(x-y)$. Analogous to the $q_{ij}$-Fock space of Bozejko and Speicher, we have field operators arising as the sum of the creation and annihilation operators. These operators generate a von Neumann algebra analogous to the free group factors, and we will show that they are factors which do not have property $Γ$. It was pointed out to us by an anonymous referee that this is a special case of a theorem of Krolak.
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