Gröbner-shirshov Bases for Coxeter Groups I *
نویسندگان
چکیده
A conjecture of Gröbner-Shirshov basis of any Coxeter group has proposed by L.A. Bokut and L.-S. Shiao [4]. In this paper, we give an example to show that the conjecture is not true in general. We list all possible nontrivial inclusion compositions when we deal with the general cases of the Coxeter groups. We give a Gröbner-Shirshov basis of a Coxeter group which is without nontrivial inclusion compositions mentioned the above.
منابع مشابه
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 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 کاملRelative 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 کاملGröbner-Shirshov Bases for Lie Algebras: after A. I. Shirshov
In this paper, we review Shirshov’s method for free Lie algebras invented by him in 1962 [17] which is now called the Gröbner-Shirshov bases theory.
متن کاملGröBner-Shirshov Bases for Dialgebras
In this paper, we define the Gröbner-Shirshov bases for a dialgebra. The composition-diamond lemma for dialgebras is given then. As a result, we obtain a Gröbner-Shirshov basis for the universal enveloping algebra of a Leibniz algebra.
متن کامل