Averaging algebras, rewriting systems and Gröbner-Shirshov bases

2016/01/04 by Xing Gao, Tianjie Zhang, Gao, Xing +1 · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1601.00553

openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain a sufficient and necessary condition for the confluence. We supply the relationship between rewriting systems and Grobner-Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a non-empty set.

Citations

• An Algebraic Study of Averaging Operators
• Some apparent connection between Baxter and averaging operators

Cited by

• Algebraic identities for linear operators on associative triple systems (long version)
• A further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras
• Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras

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