Gröbner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras

Abstract

In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner-Shirshov bases and linear bases of free commutative Rota-Baxter algebra, free commutative $λ$-differential algebra and free commutative $λ$-differential Rota-Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative $Ω$-words.

15pages. arXiv admin note: text overlap with arXiv:0805.0640