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)].
Reviewer: T.Brzeziński (York)
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) |
