Loop of formal diffeomorphisms and Faà di Bruno coloop bialgebra

  title={Loop of formal diffeomorphisms and Fa{\`a} di Bruno coloop bialgebra},
  author={Alessandra Frabetti and Ivan P. Shestakov},
  journal={Advances in Mathematics},

Faà di Bruno's formula and inversion of power series

Trees and Fa\`a di Bruno's formula

Faa di Bruno's formula gives an expression for the higher order derivatives of the composition of two real-valued functions. Various higher dimensional generalisations have since appeared in the

A retrospect of the research in nonassociative algebras in IME-USP

The aim of this paper is to give an overview of the participation of our research group in the development of nonassociative algebras.



Non-commutative Hopf algebra of formal diffeomorphisms

Formal multiplications, bialgebras of distributions and nonassociative Lie theory

We describe the general nonassociative version of Lie theory that relates unital formal multiplications (formal loops), Sabinin algebras and nonassociative bialgebras.Starting with a formal

Co-Moufang Deformations of the Universal Enveloping Algebra of the Algebra of Traceless Octonions

By means of graphical calculus we prove that, over fields of characteristic zero, any bialgebra deformation of the universal enveloping algebra of the algebra of traceless octonions satisfying the

Multiplicative Renormalization and Hopf Algebras

We derive the existence of Hopf subalgebras generated by Green’s functions in the Hopf algebra of Feynman graphs of a quantum field theory. This means that the coproduct closes on these Green’s

Combinatorial Hopf algebras

We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the cofree coalgebra

Combinatorial Hopf algebras from renormalization

In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the


Abstract This article explores a generalization of the algebraic theory of formal languages. Having, as starting point, the work of T. Colcombet on cost functions and stabilization monoids, and of

Quantum groups and representations of monoidal categories

  • David N. Yettera
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1990
This paper is intended to make explicit some aspects of the interactions which have recently come to light between the theory of classical knots and links, the theory of monoidal categories,

Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure