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arXiv · 2109.07595

Garside Theory: a Composition--Diamond Lemma Point of View

Viktor Lopatkin
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Abstract

This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show in some cases the greedy normal form is exactly a Gr\"obner--Shirshov normal form and a family of a left-cancellative category is a Garside family, if and only if a suitable set of reductions is confluent up to some congruence on words.

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Viktor Lopatkin. 2021-09-15. Garside Theory: a Composition--Diamond Lemma Point of View. https://arxiv.org/abs/2109.07595

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