منابع مشابه
On Differential Rota-baxter Algebras
Abstract. A Rota-Baxter operator of weight λ is an abstraction of both the integral operator (when λ = 0) and the summation operator (when λ = 1). We similarly define a differential operator of weight λ that includes both the differential operator (when λ = 0) and the difference operator (when λ = 1). We further consider an algebraic structure with both a differential operator of weight λ and a...
متن کاملAn Identity in Rota-baxter Algebras
We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.
متن کاملFree Rota – Baxter Algebras and Rooted Trees
A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third ...
متن کاملRota-baxter Operators on Generalized Power Series Rings
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.
متن کاملRota–baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota–Baxter algebras enters the scene. In this note we revi...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2016
ISSN: 1370-1444
DOI: 10.36045/bbms/1483671622