Some new results on Gröbner-Shirshov bases
In this survey article, we report some new results of Gröbner-Shirshov bases, including new Composition-Diamond lemmas and some applications of some known Composition-Diamond lemmas.
math.RA↗
arXiv subjects
K. P. Shum
Publications and source records attributed to K. P. Shum.
Markov 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 Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.
math.GR↗
Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$
Let $U_q(A_N)$ be the Drinfeld-Jimbo quantum group of type $A_N$. In this paper, by using Groebner-Shirshov bases, we give a simple (but not short) proof of the Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$.
math.RA↗