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

TL;DR

This paper introduces a three-parameter Hopf algebra deformation that connects the algebra of Feynman-like diagrams with other significant Hopf algebras, revealing new relationships in mathematical physics.

Contribution

It constructs a novel three-parameter Hopf deformation of the algebra of Feynman-like diagrams, linking it to MQSym and polyzeta functions.

Findings

Deformation reduces to original algebra and MQSym under specific parameters.

Reproduces product law of polyzeta functions.

Establishes connections between different Hopf algebras in physics.

Abstract

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.