Gröbner-Shirshov basis for the braid group in the Artin-Garside generators

• Autores: L. A. Bokut
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 6-7, 2008, págs. 397-405
• Idioma: inglés
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• Resumen

  • Using [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 Bn+1 in the Artin�Garside generators. We prove that S-irreducible words of the Bn+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 of positive braids is a subsemigroup into Bn+1.