Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
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 t...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2023 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2023
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211878 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces. Joscha Diehl, Malte Gerhold and Nicolas Gilliers. SIGMA 19 (2023), 006, 50 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862623578476773376 |
|---|---|
| author | Diehl, Joscha Gerhold, Malte Gilliers, Nicolas |
| author_facet | Diehl, Joscha Gerhold, Malte Gilliers, Nicolas |
| citation_txt | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces. Joscha Diehl, Malte Gerhold and Nicolas Gilliers. SIGMA 19 (2023), 006, 50 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 independence 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.
|
| first_indexed | 2026-03-14T14:20:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211878 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T14:20:01Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Diehl, Joscha Gerhold, Malte Gilliers, Nicolas 2026-01-14T09:56:10Z 2023 Shuffle Algebras and Non-Commutative Probability for Pairs of Faces. Joscha Diehl, Malte Gerhold and Nicolas Gilliers. SIGMA 19 (2023), 006, 50 pages 1815-0659 2020 Mathematics Subject Classification: 46L53; 60A05; 18M05; 46L54; 16T05; 16T10; 16T30 arXiv:2201.11747 https://nasplib.isofts.kiev.ua/handle/123456789/211878 https://doi.org/10.3842/SIGMA.2023.006 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 independence 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. The authors would like to thank Kurusch Ebrahimi-Fard, Michael Schürmann, and Philipp Varšo for many discussions on moment-cumulant relations and related algebraic questions. We thank the anonymous referees for their valuable feedback. M.G. was supported by the German Research Foundation (DFG) grant no. 397960675; part of his work was carried out during the tenure of an ERCIM ‘Alain Bensoussan’ Fellowship Programme. J.D. and N.G. are supported by the trilateral (DFG/ANR/JST) grant “EnhanceD Data stream Analysis with the Signature Method”. N.G. is supported by ANR “STARS”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Shuffle Algebras and Non-Commutative Probability for Pairs of Faces Article published earlier |
| spellingShingle | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces Diehl, Joscha Gerhold, Malte Gilliers, Nicolas |
| title | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces |
| title_full | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces |
| title_fullStr | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces |
| title_full_unstemmed | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces |
| title_short | Shuffle Algebras and Non-Commutative Probability for Pairs of Faces |
| title_sort | shuffle algebras and non-commutative probability for pairs of faces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211878 |
| work_keys_str_mv | AT diehljoscha shufflealgebrasandnoncommutativeprobabilityforpairsoffaces AT gerholdmalte shufflealgebrasandnoncommutativeprobabilityforpairsoffaces AT gilliersnicolas shufflealgebrasandnoncommutativeprobabilityforpairsoffaces |