论文标题
加权Cuntz代数
Weighted Cuntz Algebras
论文作者
论文摘要
我们研究$ c^*$ - 代数$ \ MATHCAL {t}/\ MATHCAL {k} $，其中$ \ Mathcal {t} $是$ c^*$ - 由$ d $ d $加权转移产生的$ c^*$ - $ \ \ nathbb {c} c}^d $， $ \ MATHCAL {f}（\ MATHBB {C}^d）$，（其中重量由矩阵$ z_k \ in m_ {d^k}中的序列$ \ {z_k \} $给出。如果$ z_k = i $对于每个$ k $，则$ \ mathcal {t}/\ mathcal {k} $是Cuntz algebra $ \ Mathcal {o} _d $。 我们表明，$ \ Mathcal {t}/\ Mathcal {K} $对Cuntz-Pimsner代数是同构的，并使用它来找到使代数简单的条件。 我们介绍了这种类型的简单和非简单代数的示例。 我们还描述了$ c^*$ - $ \ MATHCAL {T}/\ MATHCAL {K} $的表示。
We study the $C^*$-algebra $\mathcal{T}/\mathcal{K}$ where $\mathcal{T}$ is the $C^*$-algebra generated by $d$ weighted shifts on the Fock space of $\mathbb{C}^d$, $\mathcal{F}(\mathbb{C}^d)$, ( where the weights are given by a sequence $\{Z_k\}$ of matrices $Z_k\in M_{d^k}(\mathbb{C})$) and $\mathcal{K}$ is the algebra of compact operators on the Fock space. If $Z_k=I$ for every $k$, $\mathcal{T}/\mathcal{K}$ is the Cuntz algebra $\mathcal{O}_d$. We show that $\mathcal{T}/\mathcal{K}$ is isomorphic to a Cuntz-Pimsner algebra and use it to find conditions for the algebra to be simple. We present examples of simple and of non simple algebras of this type. We also describe the $C^*$-representations of $\mathcal{T}/\mathcal{K}$.
