Gröbner-Shirshov basis for the braid group in the Artin-Garside generators
نویسنده
چکیده
In this paper, we give a Gröbner-Shirshov basis of the braid group Bn+1 in the Artin–Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup B + n + 1 is the subsemigroup in Bn+1.
منابع مشابه
Gröbner-shirshov Basis for the Braid Group in the Birman-ko-lee-garside Generators
In this paper, we obtain Gröbner-Shirshov (non-commutative Gröbner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new “Garside word” δ ([2]). It gives a new algorithm for getting the Birman-KoLee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
متن کاملGröbner-Shirshov bases for some braid groups
Presenting 2-generator Artin groups A(m) and braid groups B3 and B4 as towers of HNN extensions of free groups, we obtain Gröbner–Shirshov bases, normal forms and rewriting systems for these groups. c © 2005 Elsevier Ltd. All rights reserved.
متن کاملMarkov and Artin Normal Form Theorem for Braid Groups
In this paper we will present the results of Artin– Markov on braid groups by using the Gröbner-Shirshov basis. As a consequence we can reobtain the normal form of Artin–Markov– Ivanovsky as an easy corollary.
متن کاملGröbner-shirshov Basis for the Braid Semigroup
We found Gröbner-Shirshov basis for the braid semigroup B n+1. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.
متن کاملConjugacy problem for braid groups and Garside groups
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee [3]. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 43 شماره
صفحات -
تاریخ انتشار 2008