Geodesic
Deformations of Algebras: Twisting and Perturbations
Séminaire lotharingien de combinatoire, Tome 62 (2009-2010)

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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. 

@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},
     publisher = {mathdoc},
     volume = {62},
     year = {2009-2010},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a4/}
}
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%J Séminaire lotharingien de combinatoire
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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/