论文标题
CCR和CAR代数通过Cuntz-Toeplitz代数的路径连接
CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras
论文作者
论文摘要
对于$ q \ in \ mathbb {r} $，$ | q | < 1$ we consider the universal enveloping $C^*$-algebra of a $*$-algebra of $q$-canonical commutation relations ($q$-CCR), which is generated by $a_1, \ldots, a_n$ subject to the relations \[ a_i^* a_j = δ_{ij} 1 + q a_j a_i^* . \]它具有杰出的表示$π_f$称为fock表示，据信这是忠实的。在本文中，我们用$ \ beth_q $表示通用包裹的$ c^*$ - $ q $ -ccr的代数。 $ c^*$ - 同构$ \ beth_q \ simeq \ simeq \ beth_0 $ holds已在文献中考虑并以$ | q |证明。 <0.44 $。在本文中，我们表明$ \ beth_q \ simeq \ beth_0 $ for $ | q | <1 $。
For $q \in \mathbb{R}$, $|q| < 1$ we consider the universal enveloping $C^*$-algebra of a $*$-algebra of $q$-canonical commutation relations ($q$-CCR), which is generated by $a_1, \ldots, a_n$ subject to the relations \[ a_i^* a_j = δ_{ij} 1 + q a_j a_i^* . \] It has a distinguished representation $π_F$ called the Fock representation, which is believed to be faithful. In this article we denote the image of the universal enveloping $C^*$-algebra of $q$-CCR in the Fock representation by $\beth_q$. The question whether $C^*$-isomorphism $\beth_q \simeq \beth_0$ holds has been considered in the literature and proved for $|q| < 0.44$. In this article we show that $\beth_q \simeq \beth_0$ for $|q| < 1$.
