Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGroebner-Shirshov basis for the braid group in the Artin-Garside generators
159
0
0.0
(
0
)
Authors
L. A. Bokut
Ask ChatGPT about the research
No Arabic abstract
In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ 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 $B_{n+1}$.
rate research
Read More
In this paper, we obtain Groebner-Shirshov (non-commutative Grobner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new ``Garside word $delta$. It gives a new algorithm for getting the Birman-Ko-Lee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
We found Groebner-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.
In this paper, a Groebner-Shirshov basis for the Chinese monoid is obtained and an algorithm for the normal form of the Chinese monoid is given.
In this paper, we generalize the Shirshovs Composition Lemma by replacing the monomial order for others. By using Groebner-Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained.
In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
