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A group-theoretical approach to conditionally free cumulants
- Source :
- Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)., F. Chapoton et al. eds. Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), 31, Springer, pp.67-94, 2020, IRMA Lectures in Mathematical and Theoretical Physics, HAL
- Publication Year :
- 2020
- Publisher :
- EMS Press, 2020.
-
Abstract
- In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cumulants. This approach is based on a particular combinatorial Hopf algebra which may be characterised as a non-cocommutative generalisation of the classical unshuffle Hopf algebra. Central to our work is the resulting non-commutative shuffle algebra structure on the graded dual. It implies an extension of the classical relation between the group of Hopf algebra characters and its Lie algebra of infinitesimal characters and, among others, the appearance of new forms of adjoint actions of the group on its Lie algebra which happens to play a key role in the new algebraic understanding of conditionally free cumulants.<br />Comment: 24 pages
- Subjects :
- Pure mathematics
Group (mathematics)
Infinitesimal
Probability (math.PR)
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
010102 general mathematics
Structure (category theory)
16. Peace & justice
Hopf algebra
01 natural sciences
Shuffle algebra
Probability theory
0103 physical sciences
Lie algebra
FOS: Mathematics
0101 mathematics
Algebraic number
010306 general physics
Mathematics - Probability
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)., F. Chapoton et al. eds. Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), 31, Springer, pp.67-94, 2020, IRMA Lectures in Mathematical and Theoretical Physics, HAL
- Accession number :
- edsair.doi.dedup.....5b5de919ffb374903460618080afd43d