Connes, Alain; Kreimer, Dirk Hopf algebras, renormalization and noncommutative geometry. (English) Zbl 0932.16038 Commun. Math. Phys. 199, No. 1, 203-242 (1998). The paper establishes a relationship between the Hopf algebra \({\mathcal H}_R\) of rooted trees, introduced in the context of the renormalization procedure in quantum field theory [D. Kreimer, Adv. Theor. Math. Phys. 2, No. 2, 303–334 (1998; Zbl 1041.81087)] and the Hopf algebra \({\mathcal H}_T\) which is used to solve some computational problems arising from the transverse hypoelliptic theory of foliations in noncommutative geometry [A. Connes and H. Moscovici, Commun. Math. Phys. 198, No. 1, 199–246 (1998; Zbl 0940.58005)]. Reviewer: T.Brzeziński (York) Cited in 26 ReviewsCited in 204 Documents MSC: 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 46L87 Noncommutative differential geometry 81T05 Axiomatic quantum field theory; operator algebras 58B32 Geometry of quantum groups 58B34 Noncommutative geometry (à la Connes) Keywords:Hopf algebras; renormalization; noncommutative geometry PDF BibTeX XML Cite \textit{A. Connes} and \textit{D. Kreimer}, Commun. Math. Phys. 199, No. 1, 203--242 (1998; Zbl 0932.16038) Full Text: DOI arXiv