Categorification of Hopf algebras of rooted trees

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Categorification of Hopf algebras of rooted trees. / Kock, Joachim.

In: Central European Journal of Mathematics, Vol. 11, No. 3, 03.2013, p. 401-422.

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

Harvard

Kock, J 2013, 'Categorification of Hopf algebras of rooted trees', Central European Journal of Mathematics, vol. 11, no. 3, pp. 401-422. https://doi.org/10.2478/s11533-012-0152-1

APA

Kock, J. (2013). Categorification of Hopf algebras of rooted trees. Central European Journal of Mathematics, 11(3), 401-422. https://doi.org/10.2478/s11533-012-0152-1

Vancouver

Kock J. Categorification of Hopf algebras of rooted trees. Central European Journal of Mathematics. 2013 Mar;11(3):401-422. https://doi.org/10.2478/s11533-012-0152-1

Author

Kock, Joachim. / Categorification of Hopf algebras of rooted trees. In: Central European Journal of Mathematics. 2013 ; Vol. 11, No. 3. pp. 401-422.

Bibtex

@article{3434912c35304d8b932ced5efaaff00c,
title = "Categorification of Hopf algebras of rooted trees",
abstract = "We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec N) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to Z and collapsing H-0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring in the polynomial representation of the free monad on P.",
keywords = "Rooted trees, Hopf algebras, Categorification, Monoidal categories, Polynomial functors, Finite sets, QUANTUM-FIELD THEORY, RENORMALIZATION",
author = "Joachim Kock",
year = "2013",
month = mar,
doi = "10.2478/s11533-012-0152-1",
language = "English",
volume = "11",
pages = "401--422",
journal = "Central European Journal of Mathematics",
issn = "1895-1074",
publisher = "Versita",
number = "3",

}

RIS

TY - JOUR

T1 - Categorification of Hopf algebras of rooted trees

AU - Kock, Joachim

PY - 2013/3

Y1 - 2013/3

N2 - We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec N) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to Z and collapsing H-0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring in the polynomial representation of the free monad on P.

AB - We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec N) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to Z and collapsing H-0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring in the polynomial representation of the free monad on P.

KW - Rooted trees

KW - Hopf algebras

KW - Categorification

KW - Monoidal categories

KW - Polynomial functors

KW - Finite sets

KW - QUANTUM-FIELD THEORY

KW - RENORMALIZATION

U2 - 10.2478/s11533-012-0152-1

DO - 10.2478/s11533-012-0152-1

M3 - Journal article

VL - 11

SP - 401

EP - 422

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

SN - 1895-1074

IS - 3

ER -

ID: 331501149