论文标题
具有量子组对称性的亚产物系统。 ii
Subproduct systems with quantum group symmetry. II
论文作者
论文摘要
我们通过将上一篇论文的主要结果扩展到一般参数案例来完成对Temperley-Lieb子产品系统的分析，该系统定义了Arveson $ 2 $ shift的量子类似物。具体来说，我们表明相关的toeplitz代数是核的，为他们找到完整的关系集，证明它们与$ \ Mathbb c $等同于$ kk $，并计算了相关的cuntz-pimsner代数的$ k $ - 理论。量子对称组是由Mrozinski首先研究的量子对称组，将templeley-lieb多项式保存到重新缩放，以及它们与$ u_q（2）$的单相等性。
We complete our analysis of the Temperley-Lieb subproduct systems, which define quantum analogues of Arveson's $2$-shift, by extending the main results of the previous paper to the general parameter case. Specifically, we show that the associated Toeplitz algebras are nuclear, find complete sets of relations for them, prove that they are equivariantly $KK$-equivalent to $\mathbb C$ and compute the $K$-theory of the associated Cuntz-Pimsner algebras. A key role is played by quantum symmetry groups, first studied by Mrozinski, preserving Temperley-Lieb polynomials up to rescaling, and their monoidal equivalence to $U_q(2)$.
