论文标题
对成对的脸部的代数和非交通概率
Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
论文作者
论文摘要
可以通过考虑作用于基础尖端的希尔伯特空间的自由产品的操作员的代数代数的右手或左手表示来构建FreeNess的操作模型。同时考虑两者，也就是说，在左手和右手表示产生的代数中运算符的计算分布，在2013年LED voiculescu在2013年定义和研究了差异性，并在续集中触发了非交流性概率的扩展，现在通常称为多人效率（tworeface five）（在上面给出的两个示例）。过去几年出现了许多两面独立的例子。我们非常感兴趣的是Biboolean，Bifree和I型双孔酮独立性。在本文中，我们将K. Ebrahimi-Fard和F. Patras发起的自由，布尔和单调矩构成关系扩展到了上述的两面等效物。
One can build an operatorial model for freeness by considering either the right-handed or the left-handed representation of algebras of operators acting on the free product of the underlying pointed Hilbert spaces. Considering both at the same time, that is, computing distributions of operators in the algebra generated by the left- and right-handed representations, led Voiculescu in 2013 to define and study bifreeness and, in the sequel, triggered the development of an extension of noncommutative probability now frequently referred to as multi-faced (two-faced in the example given above). Many examples of two-faced independences emerged these past years. Of great interest to us are biBoolean, bifree and type I bimonotone independences. In this paper, we extend the preLie calculus pertaining to free, Boolean, and monotone moment-cumulant relations initiated by K. Ebrahimi-Fard and F. Patras to their above-mentioned two-faced equivalents.
