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Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Journal article
Journal
Advances in mathematics
Date of publication
2014-03-20
Volume
254
First page
79
Last page
117
DOI
https://doi.org/10.1016/j.aim.2013.12.015 Open in new window
Project funding
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Repository
http://hdl.handle.net/2117/22088 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0001870813004623 Open in new window
Abstract
We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. (C) 2013 Elsevier Inc. All rights reserved. We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.
Citation
Galvez, M.; Kock, J.; Tonks, A. Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. "Advances in mathematics", 2014, vol. 254, p. 79-117.
Keywords
Bialgebras, DUALITY, DYSON-SCHWINGER EQUATIONS, ELIMINATION, Groupoids, HOPF-ALGEBRAS, Homotopy cardinality, INSERTION, LIE-ALGEBRA, Perturbative methods of renormalisation, Polynomial functors, QUANTUM-FIELD THEORY, RENORMALIZATION-GROUP, Trees
Group of research
GEOMVAP - Geometry of Manifolds and Applications

Participants