Gröbner-Shirshov bases for some braid groups

نویسندگان

  • Leonid Bokut
  • Andrei Vesnin
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

ar X iv : 1 50 2 . 06 47 2 v 1 [ m at h . R A ] 8 N ov 2 01 4 Gröbner - Shirshov bases and PBW theorems ∗

We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

متن کامل

Gröbner-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 کامل

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

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.

متن کامل

Relative Gröbner–shirshov Bases for Algebras and Groups

The notion of a relative Gröbner–Shirshov basis for algebras and groups is introduced. The relative composition lemma and relative (composition-)diamond lemma are established. In particular, it is shown that the relative normal forms of certain groups arising from Malcev’s embedding problem are the irreducible normal forms of these groups with respect to their relative Gröbner–Shirshov bases. O...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Symb. Comput.

دوره 41  شماره 

صفحات  -

تاریخ انتشار 2006