Geodesic
Deformations of Algebras: Twisting and Perturbations
Séminaire lotharingien de combinatoire, Tome 62 (2009-2010) 
Gérard H. E. Duchamp; Christophe Tollu; Karol A. Penson; Gleb A. Koshevoy. Deformations of Algebras: Twisting and Perturbations. Séminaire lotharingien de combinatoire, Tome 62 (2009-2010). http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a4/
@article{SLC_2009-2010_62_a4,
     author = {G\'erard H. E. Duchamp and Christophe Tollu and Karol A. Penson and Gleb A. Koshevoy},
     title = {Deformations of {Algebras:} {Twisting} and {Perturbations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2009-2010},
     volume = {62},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a4/}
}
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AU  - Christophe Tollu
AU  - Karol A. Penson
AU  - Gleb A. Koshevoy
TI  - Deformations of Algebras: Twisting and Perturbations
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2010
VL  - 62
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a4/
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%A Christophe Tollu
%A Karol A. Penson
%A Gleb A. Koshevoy
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%J Séminaire lotharingien de combinatoire
%D 2009-2010
%V 62
%U http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a4/
%F SLC_2009-2010_62_a4

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The framework used to prove the multiplicative deformation of the algebra of Feynman-Bender diagrams is a twisted shifted dual law (in fact, doubly twisted). We give here a clear interpretation of its two parameters. The crossing parameter is a deformation of the tensor structure, whereas the superposition parameter is a perturbation of the shuffle coproduct which, in its turn, can be interpreted as the diagonal restriction of a superproduct. Here, we systematically explain these constructions in detail.