120 citations · 691 across the 56 of their papers we have counts for
13 papers · 1 filter
Algebraic groups in non-commutative probability theory revisited
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach…
From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras
Kurusch Ebrahimi-Fard, Frederic Patras
Gian-Carlo Rota mentioned in one of his last articles the problem of developing a theory around the notion of integration algebras, which should be dual to the one of differential…
Monomial bases and pre-Lie structure for free Lie algebras
Mahdi J. Hasan Al-Kaabi, Dominique Manchon, Frédéric Patras
In this paper, we construct a pre-Lie structure on the free Lie algebra L(E) generated by a set E, giving an explicit presentation of L(E) as the quotient of the free pre-Lie algeb…
Shuffle group laws. Applications in free probability
Kurusch Ebrahimi-Fard, Frederic Patras
Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie…
Renormalization: a quasi-shuffle approach
Frédéric Menous, Frédéric Patras
In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decompositi…
Lie theory for quasi-shuffle bialgebras
Loïc Foissy, Frédéric Patras
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be developed systematically. Quasi-shuf…