Composition-Diamond lemma for λ-differential associative algebras with multiple operators
نویسندگان
چکیده
In this paper, we establish the Composition-Diamond lemma for λ-differential associative algebras over a field K with multiple operators. As applications, we obtain Gröbner-Shirshov bases of free λ-differential Rota-Baxter algebras. In particular, linear bases of free λ-differential Rota-Baxter algebras are obtained and consequently, the free λ-differential Rota-Baxter algebras are constructed by words.
منابع مشابه
Gröbner-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 کاملComposition-Diamond lemma for associative n-conformal algebras
In this paper, we study the concept of associative n-conformal algebra over a field of characteristic 0 and establish Composition-Diamond lemma for a free associative n-conformal algebra. As an application, we construct Gröbner-Shirshov bases for Lie n-conformal algebras presented by generators and defining relations.
متن کاملComposition-Diamond Lemma for Differential Algebras
In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Gröbner-Shirshov bases for free Lie-differential algebras and free commutative-differential algebras, respectively.
متن کاملGröbner–Shirshov Bases for Irreducible sln+1-Modules
In [10], inspired by an idea of Gröbner, Buchberger discovered an effective algorithm for solving the reduction problem for commutative algebras, which is now called the Gröbner Basis Theory. It was generalized to associative algebras through Bergman’s Diamond Lemma [2], and the parallel theory for Lie algebras was developed by Shirshov [21]. The key ingredient of Shirshov’s theory is the Compo...
متن کاملAn application of non-associative Composition-Diamond lemma
In this paper, by using Gröbner–Shirshov bases for non-associative algebras invented by A. I. Shirshov in 1962, we show I. P. Shestakov’s result that any Akivis algebra can be embedded into its universal enveloping algebra.
متن کامل