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arXiv · 1601.00553

Averaging algebras, rewriting systems and Gr$ö$bner-Shirshov bases

Xing Gao·Tianjie Zhang
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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.

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Xing Gao, Tianjie Zhang. 2016-04-12. Averaging algebras, rewriting systems and Gr$ö$bner-Shirshov bases. https://arxiv.org/abs/1601.00553

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