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TitleGröbner–Shirshov basis for the Braid group in the Birman–Ko–Lee generators
Author(s) Leonid A. Bokut
TypeArticle in Journal
AbstractIn this paper, we obtain Gröbner–Shirshov (non-commutative Gröbner) bases for braid groups in the Birman–Ko–Lee generators enriched by “Garside word” δ [J. Birman, K.H. Ko, S.J. Lee, A new approach to the word and conjugacy problems for the braid groups, Adv. Math. 139 (1998) 322–353]. It gives a new algorithm for getting the Birman–Ko–Lee normal forms in braid groups, and thus a new algorithm for solving the word problem in these groups.
KeywordsGröbner–Shirshov basis, Composition-diamond lemma, Braid group, Birman–Ko–Lee generators, Birman–Ko–Lee normal form
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869308005115
LanguageEnglish
JournalJournal of Algebra
Volume321
Number2
Pages361 - 376
Year2009
Edition0
Translation No
Refereed No
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