Composition-Diamond lemma for $\lambda$-differential associative algebras with multiple operators

Abstract

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gröbner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words.

References in corpus (2)

• Rota-Baxter Algebras and Dendriform Algebras
• Free Rota-Baxter algebras and rooted trees

Cited by in corpus (2)

• Gröbner-Shirshov bases and their calculation
• Construction of free differential algebras by extending Gröbner-Shirshov bases