Shuffle代数与面对的非交换概率
Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
摘要：
人们可以通过考虑作用在底层点希尔伯特空间的自由积上的算子的代数代数的表示的右手或左手表示来建立自由度的算子模型。同时考虑到这两种情况，即计算由左手和右手表示生成的代数中算子的分布，导致Voiculescu在2013年定义和研究了双自由性，并在随后引发了非交换概率的扩展的发展，现在经常被称为多面（上面给出的例子中的双面）。在过去的几年里，出现了许多两面派的例子。我们非常感兴趣的是双布尔、双自由和I型双单调独立性。在本文中，我们扩展了preLie演算有关的自由，布尔，和单调矩累积量的关系发起的K。Ebrahimi-Fard和F.他们的两个人都是上述的双面人。
英文摘要：
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.
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。
