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Hopf algebras, renormalization and noncommutative geometry. (English) Zbl 0932.16038
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)].

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)
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