منابع مشابه
J ul 2 00 4 Properties of Free Baxter Algebras ∗
The study of free Baxter algebras was started by Rota and Cartier thirty years ago. We continue this study by applying two recent constructions of free Baxter algebras. We investigate the basic structure of a free Baxter algebra, and characterize in detail when a free Baxter algebra is a domain or a reduced algebra. We also describe the nilpotent radical of a free Baxter algebra when it is not ...
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 کاملBaxter Algebras and Hopf Algebras
George E. Andrews Department of Mathematics Pennsylvania State University University Park, PA 16802, USA ([email protected]) Li Guo Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]) William Keigher Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]...
متن کاملGröbner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras
In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Gröbner-Shirshov bases of free Rota-Baxter algebra, λ-differential algebra and λ-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2000
ISSN: 0001-8708
DOI: 10.1006/aima.1999.1898