Normal forms in braid groups with respect to some Gröbner–Shirshov basis

DOI10.1142/S0218216520430051zbMath1486.20045OpenAlexW3112200206MaRDI QIDQ4965600

Xing Chen, Xuezhi Zhao

Publication date: 6 March 2021

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218216520430051

zbMATH Keywords

normal formword problembraid groupGröbner-Shirshov basisirreducible word

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Braid groups; Artin groups (20F36)

Cites Work

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• Gröbner-Shirshov basis for the braid group in the Artin-Garside generators.
• Gröbner-Shirshov basis for the braid group in the Birman-Ko-Lee generators.
• A new approach to the word and conjugacy problems in the braid groups
• Factoring products of braids via garside normal form
• Gröbner-Shirshov bases for some braid groups.
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Braids and permutations
• ALGORITHMS FOR POSITIVE BRAIDS
• Groebner-Shirshov basis for the braid semigroup
• Some Algorithmic Problems for Lie Algebras
• THE BRAID GROUP AND OTHER GROUPS

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