Séminaire Lotharingien de Combinatoire, B62e (2010), 14 pp.

Gérard H. E. Duchamp, Christophe Tollu, Karol A. Penson and Gleb A. Koshevoy

Deformations of Algebras: Twisting and Perturbations

Abstract. 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.

Received: April 28, 2009. Revised: September 6, 2010. Accepted: November 26, 2010. Final Version: November 30, 2010.

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