Some results on continuous deformed free group factors

Details Some results on continuous deformed free group factors Some results on continuous deformed free group factors

2012-03-09

arxiv.org/abs/1203.2176v3

Mathematics

Operator Algebras

13 pages. This fixes numerous typographical errors and clarifies exposition

Scientific paper

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 $a(x)a^+(y)-Q(x,y)a^+(y)a(x)=\delta(x-y)$. 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 $\Gamma$.

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