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Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
Joscha Diehla, Malte Gerholdab, Nicolas Gilliersac a Universität Greifswald, Institut für Mathematik und Informatik, Walther-Rathenau-Str. 47, 17489 Greifswald, Germany
b Norwegian University of Science and Technology (NTNU),
Department of Mathematical Sciences, 7491 Trondheim, Norway
c Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
Аннотация:
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.
Ключевые слова:
shuffle algebras, non-commutative probability, cumulants, multi-faced, Möbius category.
Поступила: 30 марта 2022 г.; в окончательном варианте 10 января 2023 г.; опубликована 31 января 2023 г.
Образец цитирования:
Joscha Diehl, Malte Gerhold, Nicolas Gilliers, “Shuffle Algebras and Non-Commutative Probability for Pairs of Faces”, SIGMA, 19 (2023), 006, 50 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1901 https://www.mathnet.ru/rus/sigma/v19/p6
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