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TitleGröbner–Shirshov basis for the braid group in the Artin–Garside generators
Author(s) Leonid A. Bokut
TypeArticle in Journal
AbstractUsing [Bokut, L., Fong, Y., Ke, W.-F., Shiao, L-S., 2003. Gröbner–Shirshov basis for the braid semigroup. In: Shum, K.-P. (Ed.), Advances in Algebra and Related Topics. Proceedings of the ICM2002 Satellite Conference on Algebra, Hong Kong. World Scientific, River Edge, pp. 14–25], we find a Gröbner–Shirshov basis S for the braid group B_n+1 in the Artin–Garside generators. We prove that S -irreducible words of the B_n+1 coincide with the Garside normal form words. It gives a new proof of the uniqueness of the Garside normal form of a word, as well as a new proof that the semigroup B_n+1^+ of positive braids is a subsemigroup into B_n+1.
KeywordsGröbner–Shirshov basis, Braid group, Garside normal form
URL http://www.sciencedirect.com/science/article/pii/S0747717107001447
JournalJournal of Symbolic Computation
Pages397 - 405
NoteSpecial issue on ASCM 2005
Translation No
Refereed No