Gröbner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras
نویسندگان
چکیده
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 the recent results obtained to those obtained by K. Ebrahimi-Fard – L. Guo, and L. Guo – W. Keigher by using other methods.
منابع مشابه
Composition-Diamond lemma for λ-differential associative algebras with multiple operators
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 ...
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