A Three Parameter Hopf Deformation of the Algebra of Feynman-like Diagrams

We construct a three-parameter deformation of the Hopf algebra $\text{LDIAG}$. This is the algebra that appears in an expansion in terms of Feynman-like diagrams of the {\em product formula} in a simplified version of Quantum Field Theory. This new algebra is a true Hopf deformation which reduces to $\text{LDIAG}$ for some parameter values and to the algebra of Matrix Quasi-Symmetric Functions ($\text{MQS}$) for others, and thus relates $\text{LDIAG}$ to other Hopf algebras of contemporary physics. Moreover, there is an onto linear mapping preserving products from our algebra to the algebra of Euler-Zagier sums.