Title: The deformed LDIAG Hopf algebra and polyzetas

Author 1 (CONTACT AUTHOR)
 Name: Gérard  Duchamp
 Org: Université Paris 13 - CNRS
 Country: France
 Email:ghed@lipn.univ-paris13.fr

Contact Alt Email: ghed@lipn.univ-paris13.fr
Contact Phone:

Keywords: Hopf algebra, Feyman diagrams

Abstract: We first show that pre-Feyman diagrams naturally arise from
the diagrammatic expansion of a certain product formula (from the "QFT
of partitions") applied to two one-parameter formal groups.
These diagrams span a vector space which can be endowed with the structure
of a Hopf algebra so that evaluations are compatible with composition
(product) and decomposition (coproduct).
This Hopf algebra (DIAG, linked to unordered set partitions)
is commutative and of limited application ; however, its non-commutative
analogue (LDIAG, linked with ordered set partitions) is free and a
three-parameter deformation is sufficiently rich to specialize
to matrix non-commutative quasi-symmetric functions and polyzeta
functions. We propose to explain this last point in detail and show that
this deformation also provides a new insight relevant to the deformation
of polyzeta functions.