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Volumn 218, Issue 1, 2008, Pages 136-162

Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations

Author keywords

Combinatorial Dyson Schwinger equation; Fa di Bruno Hopf algebra; Hopf algebra of (planar) rooted trees

Indexed keywords


EID: 40849136305     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.12.003     Document Type: Article
Times cited : (56)

References (20)
  • 1
    • 33646514658 scopus 로고    scopus 로고
    • Zimmermann type cancellation in the free Faà di Bruno algebra
    • math/0504436
    • Anshelevich M., G. Effros E., and Popa M. Zimmermann type cancellation in the free Faà di Bruno algebra. J. Funct. Anal. 237 1 (2006) 76-104. math/0504436
    • (2006) J. Funct. Anal. , vol.237 , Issue.1 , pp. 76-104
    • Anshelevich, M.1    G. Effros, E.2    Popa, M.3
  • 2
    • 35348877778 scopus 로고    scopus 로고
    • Hopf algebras in renormalization theory: locality and Dyson-Schwinger equations from Hochschild cohomology
    • math/0506190
    • Bergbauer C., and Kreimer D. Hopf algebras in renormalization theory: locality and Dyson-Schwinger equations from Hochschild cohomology. IRMA Lect. Math. Theor. Phys. 10 (2006) 133-164. math/0506190
    • (2006) IRMA Lect. Math. Theor. Phys. , vol.10 , pp. 133-164
    • Bergbauer, C.1    Kreimer, D.2
  • 3
    • 0034336368 scopus 로고    scopus 로고
    • Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees
    • hep-th/0001202
    • Broadhurst D.J., and Kreimer D. Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees. Comm. Math. Phys. 215 1 (2000) 217-236. hep-th/0001202
    • (2000) Comm. Math. Phys. , vol.215 , Issue.1 , pp. 217-236
    • Broadhurst, D.J.1    Kreimer, D.2
  • 4
    • 8144231442 scopus 로고    scopus 로고
    • Trees, renormalization and differential equations
    • Brouder C. Trees, renormalization and differential equations. BIT 44 3 (2004) 425-438
    • (2004) BIT , vol.44 , Issue.3 , pp. 425-438
    • Brouder, C.1
  • 5
    • 0032257297 scopus 로고    scopus 로고
    • Hopf algebras, Renormalization and Noncommutative geometry
    • hep-th/9808042
    • Connes A., and Kreimer D. Hopf algebras, Renormalization and Noncommutative geometry. Comm. Math. Phys. 199 1 (1998) 203-242. hep-th/9808042
    • (1998) Comm. Math. Phys. , vol.199 , Issue.1 , pp. 203-242
    • Connes, A.1    Kreimer, D.2
  • 6
    • 0032210257 scopus 로고    scopus 로고
    • Hopf algebras, cyclic cohomology and the transverse index theorem
    • math.DG/9806109
    • Connes A., and Moscovici H. Hopf algebras, cyclic cohomology and the transverse index theorem. Comm. Math. Phys. 198 1 (1998) 199-246. math.DG/9806109
    • (1998) Comm. Math. Phys. , vol.198 , Issue.1 , pp. 199-246
    • Connes, A.1    Moscovici, H.2
  • 7
    • 0041862792 scopus 로고    scopus 로고
    • Combinatorics of rooted trees and Hopf algebras
    • math.CO/0201253
    • Hoffman M.E. Combinatorics of rooted trees and Hopf algebras. Trans. Amer. Math. Soc. 355 9 (2003) 3795-3811. math.CO/0201253
    • (2003) Trans. Amer. Math. Soc. , vol.355 , Issue.9 , pp. 3795-3811
    • Hoffman, M.E.1
  • 8
    • 0036759247 scopus 로고    scopus 로고
    • Finite-dimensional comodules over the Hopf algebra of rooted trees
    • math.QA/0105210
    • Foissy L. Finite-dimensional comodules over the Hopf algebra of rooted trees. J. Algebra 255 1 (2002) 85-120. math.QA/0105210
    • (2002) J. Algebra , vol.255 , Issue.1 , pp. 85-120
    • Foissy, L.1
  • 9
    • 40849104717 scopus 로고    scopus 로고
    • Les algèbres de Hopf des arbres enracinés, I
    • Loïc Foissy O. Les algèbres de Hopf des arbres enracinés, I. Bull. Sci. Math. 126 (2002) 193-239
    • (2002) Bull. Sci. Math. , vol.126 , pp. 193-239
    • Loïc Foissy, O.1
  • 10
    • 0043104439 scopus 로고    scopus 로고
    • Les algèbres de Hopf des arbres enracinés, II
    • Foissy L. Les algèbres de Hopf des arbres enracinés, II. Bull. Sci. Math. 126 (2002) 249-288
    • (2002) Bull. Sci. Math. , vol.126 , pp. 249-288
    • Foissy, L.1
  • 11
    • 0038238179 scopus 로고    scopus 로고
    • Comparison of Hopf algebras on trees
    • Holtkamp R. Comparison of Hopf algebras on trees. Arch. Math. (Basel) 80 4 (2003) 368-383
    • (2003) Arch. Math. (Basel) , vol.80 , Issue.4 , pp. 368-383
    • Holtkamp, R.1
  • 12
    • 33646035766 scopus 로고    scopus 로고
    • On the Hopf algebra structure of perturbative quantum field theories
    • q-alg/9707029
    • Kreimer D. On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2 2 (1998) 303-334. q-alg/9707029
    • (1998) Adv. Theor. Math. Phys. , vol.2 , Issue.2 , pp. 303-334
    • Kreimer, D.1
  • 13
    • 0033426909 scopus 로고    scopus 로고
    • On overlapping divergences
    • hep-th/9810022
    • Kreimer D. On overlapping divergences. Comm. Math. Phys. 204 3 (1999) 669-689. hep-th/9810022
    • (1999) Comm. Math. Phys. , vol.204 , Issue.3 , pp. 669-689
    • Kreimer, D.1
  • 14
    • 0036239309 scopus 로고    scopus 로고
    • Combinatorics of (perturbative) quantum field theory
    • hep-th/0010059
    • Kreimer D. Combinatorics of (perturbative) quantum field theory. Phys. Rep. 4-6 (2002) 387-424. hep-th/0010059
    • (2002) Phys. Rep. , vol.4-6 , pp. 387-424
    • Kreimer, D.1
  • 15
    • 35348831582 scopus 로고    scopus 로고
    • Dyson-Schwinger Equations: From Hopf Algebras to Number Theory
    • Amer. Math. Soc., Providence, RI
    • Kreimer D. Dyson-Schwinger Equations: From Hopf Algebras to Number Theory. Fields Inst. Commun. vol. 50 (2007), Amer. Math. Soc., Providence, RI
    • (2007) Fields Inst. Commun. , vol.50
    • Kreimer, D.1
  • 16
    • 33749460339 scopus 로고    scopus 로고
    • An étude in non-linear Dyson-Schwinger equations
    • Kreimer D., and Yeats K. An étude in non-linear Dyson-Schwinger equations. Nuclear Phys. B Proc. Suppl. 160 (2006) 116-121
    • (2006) Nuclear Phys. B Proc. Suppl. , vol.160 , pp. 116-121
    • Kreimer, D.1    Yeats, K.2
  • 17
    • 0000721182 scopus 로고
    • Duality between quasi-symmetric functions and the Solomon descent algebra
    • Malvenuto C., and Reutenauer C. Duality between quasi-symmetric functions and the Solomon descent algebra. J. Algebra 177 3 (1995) 967-982
    • (1995) J. Algebra , vol.177 , Issue.3 , pp. 967-982
    • Malvenuto, C.1    Reutenauer, C.2
  • 18
    • 0000859132 scopus 로고
    • On the structure of Hopf algebras
    • W. Milnor J., and C. Moore J. On the structure of Hopf algebras. Ann. of Math. (2) 81 (1965) 211-264
    • (1965) Ann. of Math. (2) , vol.81 , pp. 211-264
    • W. Milnor, J.1    C. Moore, J.2
  • 19
    • 0003306141 scopus 로고    scopus 로고
    • Enumerative Combinatorics, vol. 1
    • Cambridge University Press, Cambridge
    • P. Stanley R. Enumerative Combinatorics, vol. 1. Cambridge Stud. Adv. Math. vol. 49 (1997), Cambridge University Press, Cambridge
    • (1997) Cambridge Stud. Adv. Math. , vol.49
    • P. Stanley, R.1
  • 20
    • 0013386138 scopus 로고    scopus 로고
    • Enumerative Combinatorics, vol. 2
    • Cambridge University Press, Cambridge
    • Stanley R.P. Enumerative Combinatorics, vol. 2. Cambridge Stud. Adv. Math. vol. 62 (1999), Cambridge University Press, Cambridge
    • (1999) Cambridge Stud. Adv. Math. , vol.62
    • Stanley, R.P.1


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