论文标题
$ c^*$ - 右lcm monoids的$ c^*$代数的无准动态状态
KMS states of quasi-free dynamics on $C^*$-algebras of product systems over right LCM monoids
论文作者
论文摘要
我们通过表明NICA-TOEPLITZ $ C^*$ - 右LCM MONOID在Nica-Toeplitz $ c^*$上的代数必须满足其在良好的系统中满足其不平等的系统的良好状态，因此，我们将AFSAR，LARSEN和NESHVEYEV的最新结果概括为产品系统对产品系统的最新结果，这是对产品系统的平衡状态。我们证明，将这种阳性条件的降低到有限的不平等亚集中是有效的，对于正确包括有限型Artin monoids的更广泛的单型物体有效，回答了他们的工作中留下的问题。我们的主要技术工具是一种结合生成的树，该树建立在Boyu li最近为散布表示的膨胀的建筑中建模。我们还将阳性条件的降低降低到由某个最小的子集引起的不平等现象，该子集可能不是有限的，但具有对所有Noetherian右LCM Monoids持有的优势，我们提出了一个例子，由有限的ARTIN MONOID引起，该型号是由有限的ARTIN MONOID引起的，该型号在其反向温度空间中表现出一个空隙。
We generalise recent results of Afsar, Larsen and Neshveyev for product systems over quasi-lattice orders by showing that the equilibrium states of quasi-free dynamics on the Nica-Toeplitz $C^*$-algebras of product systems over right LCM monoids must satisfy a positivity condition encoded in a system of inequalities satisfied by their restrictions to the coefficient algebra. We prove that the reduction of this positivity condition to a finite subset of inequalities is valid for a wider class of monoids that properly includes finite-type Artin monoids, answering a question left open in their work. Our main technical tool is a combinatorially generated tree modelled on a recent construction developed by Boyu Li for dilations of contractive representations. We also obtain a reduction of the positivity condition to inequalities arising from a certain minimal subset that may not be finite but has the advantage of holding for all Noetherian right LCM monoids, and we present an example, arising from a finite-type Artin monoid, that exhibits a gap in its inverse temperature space.
