A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams

Gérard Henry Edmond Duchamp (1) , Allan I. Solomon (2) , Pawel Blasiak (2) , Karol A. Penson (2) , Andrzej Horzela (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

We construct a three parameter deformation of the Hopf algebra $\mathbf{LDIAG}$. This new algebra is a true Hopf deformation which reduces to $\mathbf{LDIAG}$ on one hand and to $\mathbf{MQSym}$ on the other, relating $\mathbf{LDIAG}$ to other Hopf algebras of interest in contemporary physics. Further, its product law reproduces that of the algebra of polyzeta functions.

Keywords: Hopf deformation; Algebra of diagrams

Domains: Symbolic Computation [cs.SC]; Mathematical Physics [math-ph]

Gérard Henry Edmond Duchamp, Allan I. Solomon, Pawel Blasiak, Karol A. Penson, Andrzej Horzela. A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams. 2006. ⟨hal-00095588v1⟩