江苏大学夏利猛作了一场题为“On the center of the quantized enveloping algebra of a semisimple Lie algebra(在一个半单李代数的量子化包络代数的中心)”的讲座,江苏大学拥有动力工程及工程热物理、农业工程、材料科学与工程、食品科学与工程、新能源汽车、生物技术及其医药转化高校优势学科。在职研究生讲座的主要内容是:
设g是一个复杂的简单的有限维李代数和UQ(克)詹特伦与q是一般意义上的量化的包络代数。正如[LWP,WWL]连续工作中,我们证明了量子群UQ(G)的中心Z(UQ(G))同构于幺半群代数,和Z(UQ(G))是多项式代数当且仅当g为A1,BN,CN,D2K+2,E7,E8,F4和G2。事实证明,当G的类型是DN与n个奇数,则Z(UQ(G))同构与n + 1个变量和一个关系多项式代数的商代数,和而当g为E6,那么Z( UQ(G))同构于多项式代数与14个变量和八个关系商代数。
Let g be a complex simple finite dimensional Lie algebra and Uq(g) the quantized enveloping algebra in Jantzen's sense with q being generic. As a continuous work in [LWP, WWL], we prove that the center Z(Uq(g)) of the quantum group Uq(g) is isomorphic to a monoid algebra, and Z(Uq(g)) is a polynomial algebra if and only if g is of type A1, Bn, Cn, D2k+2, E7, E8, F4 and G2. It turns out that when g is of type Dn with n odd then Z(Uq(g)) is isomorphic to a quotient algebra of polynomial algebra with n+1 variables and one relation, and while when g is of type E6 then Z(Uq(g)) is isomorphic to a quotient algebra of polynomial algebra with 14 variables and eight relations.