论文标题
在代数上$ u_q^{\ pm}（a_n）$：从建设性计算观点
On The Algebras $U_q^{\pm}(A_N)$: From A Constructive-Computational Viewpoint
论文作者
论文摘要
令$ u_q^+（a_n）$（分别$ u_q^ - （a_n）$）为$（+）$ - part（resp。$（ - ）$ - $（ - $ - 零件），$ k $上的drinfeld-jimbo量子$ a_n $类型$ a_n $。关于Jimbo关系和PBW $ K $ -BASIS $ {\ cal B} $的$ u_q^+（a_n）$（yamane建立的resp。u_q^ - （a_n）$），显示出来，通过构建适当的单级订购$ \ on $ {$ cal b} $ _________________________________________________（ $ u_q^ - （a_n）$）是可解决的多项式代数。因此，可以以建设性的计算方式建立和实现其模块的$ u_q^+（a_n）$（$ u_q^ - （a_n）$）的进一步结构属性。
Let $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) be the $(+)$-part (resp. $(-)$-part) of the Drinfeld-Jimbo quantum group of type $A_N$ over a field $K$. With respect to Jimbo relations and the PBW $K$-basis ${\cal B}$ of $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) established by Yamane, it is shown, by constructing an appropriate monomial ordering $\prec$ on ${\cal B}$, that $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) is a solvable polynomial algebra. Consequently, further structural properties of $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) and their modules may be established and realized in a constructive-computational way.
