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arXiv · 1601.04254

Rota's Classification Problem, rewriting systems and Gr\"obner-Shirshov bases

Xing Gao·Li Guo
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Abstract

In this paper we revisit Rota's Classification Problem on classifying algebraic identities for linear operator. We reformulate Rota's Classification Problem in the contexts of rewriting systems and Gr\"obner-Shirshov bases, through which Rota's Classification Problem amounts to the classification of operators, given by their defining operator identities, that give convergent rewriting systems or Gr\"obner-Shirshov bases. Relationship is established between the reformulations in terms of rewriting systems and that of Gr\"obner-Shirshov bases. We provide an effective condition that gives Gr\"obner-Shirshov operators and obtain a new class of Gr\"obner-Shirshov operators.

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Xing Gao, Li Guo. 2016-01-17. Rota's Classification Problem, rewriting systems and Gr\"obner-Shirshov bases. https://arxiv.org/abs/1601.04254

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