Rota-Baxter operators and Bernoulli polynomials
نویسندگان
چکیده
منابع مشابه
Rota-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.
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Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. We develop new identities and principles in the theory of ...
متن کاملOn 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 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 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.
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ژورنال
عنوان ژورنال: Communications in Mathematics
سال: 2021
ISSN: 2336-1298
DOI: 10.2478/cm-2021-0001