Cuntz代数的单调表示与马尔可夫测度
Monic representations of the Cuntz algebra and Markov measures
摘要：
研究了Cuntz代数$Ø_N$的表示.虽然，对于固定的$N$，已知$Ø_N$的表示的等价类的集合不具有Borel截面，但是存在可以被分类的表示的各种子类。我们研究了$Ø_N$的幺一表示，它的正则交换子代数具有循环向量。我们证明了$Ø_N$有一个包含所有正幺半群表示的泛表示.一大类monic表示的例子是基于马尔可夫测度。我们对它们进行了分类，并由此得到不同的参数产生相互奇异的马尔可夫测度，推广了Kakutani的经典结果。基于角谷测度的幺一表示恰好是具有一维循环$S_i^*$不变空间的幺一表示。
英文摘要：
We study representations of the Cuntz algebras $Ø_N$. While, for fixed $N$, the set of equivalence classes of representations of $Ø_N$ is known not to have a Borel cross section, there are various subclasses of representations which can be classified. We study monic representations of $Ø_N$, that have a cyclic vector for the canonical abelian subalgebra. We show that $Ø_N$ has a certain universal representation which contains all positive monic representations. A large class of examples of monic representations is based on Markov measures. We classify them and as a consequence we obtain that different parameters yield mutually singular Markov measure, extending the classical result of Kakutani. The monic representations based on the Kakutani measures are exactly the ones that have a one-dimensional cyclic $S_i^*$-invariant space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
