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

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Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees. / Galvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew.

In: Advances in Mathematics, Vol. 254, 20.03.2014, p. 79-117.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Galvez-Carrillo, I, Kock, J & Tonks, A 2014, 'Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees', Advances in Mathematics, vol. 254, pp. 79-117. https://doi.org/10.1016/j.aim.2013.12.015

APA

Galvez-Carrillo, I., Kock, J., & Tonks, A. (2014). Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees. Advances in Mathematics, 254, 79-117. https://doi.org/10.1016/j.aim.2013.12.015

Vancouver

Galvez-Carrillo I, Kock J, Tonks A. Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees. Advances in Mathematics. 2014 Mar 20;254:79-117. https://doi.org/10.1016/j.aim.2013.12.015

Author

Galvez-Carrillo, Imma ; Kock, Joachim ; Tonks, Andrew. / Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees. In: Advances in Mathematics. 2014 ; Vol. 254. pp. 79-117.

Bibtex

@article{de950612c48b4cd8a72bd088747302dc,
title = "Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees",
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.",
keywords = "Trees, Groupoids, Homotopy cardinality, Polynomial functors, Bialgebras, Perturbative methods of renormalisation, DYSON-SCHWINGER EQUATIONS, QUANTUM-FIELD THEORY, HOPF-ALGEBRAS, RENORMALIZATION-GROUP, LIE-ALGEBRA, ELIMINATION, INSERTION, DUALITY",
author = "Imma Galvez-Carrillo and Joachim Kock and Andrew Tonks",
year = "2014",
month = mar,
day = "20",
doi = "10.1016/j.aim.2013.12.015",
language = "English",
volume = "254",
pages = "79--117",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees

AU - Galvez-Carrillo, Imma

AU - Kock, Joachim

AU - Tonks, Andrew

PY - 2014/3/20

Y1 - 2014/3/20

N2 - 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.

AB - 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.

KW - Trees

KW - Groupoids

KW - Homotopy cardinality

KW - Polynomial functors

KW - Bialgebras

KW - Perturbative methods of renormalisation

KW - DYSON-SCHWINGER EQUATIONS

KW - QUANTUM-FIELD THEORY

KW - HOPF-ALGEBRAS

KW - RENORMALIZATION-GROUP

KW - LIE-ALGEBRA

KW - ELIMINATION

KW - INSERTION

KW - DUALITY

U2 - 10.1016/j.aim.2013.12.015

DO - 10.1016/j.aim.2013.12.015

M3 - Journal article

VL - 254

SP - 79

EP - 117

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 331500897