江蘇大學(xué)夏利猛作了一場題為“On the center of the quantized enveloping algebra of a semisimple Lie algebra(在一個(gè)半單李代數(shù)的量子化包絡(luò)代數(shù)的中心)”的講座，江蘇大學(xué)擁有動(dòng)力工程及工程熱物理、農(nóng)業(yè)工程、材料科學(xué)與工程、食品科學(xué)與工程、新能源汽車、生物技術(shù)及其醫(yī)藥轉(zhuǎn)化高校優(yōu)勢(shì)學(xué)科。在職研究生講座的主要內(nèi)容是：

　　設(shè)g是一個(gè)復(fù)雜的簡單的有限維李代數(shù)和UQ(克)詹特倫與q是一般意義上的量化的包絡(luò)代數(shù)。正如[LWP，WWL]連續(xù)工作中，我們證明了量子群UQ(G)的中心Z(UQ(G))同構(gòu)于幺半群代數(shù)，和Z(UQ(G))是多項(xiàng)式代數(shù)當(dāng)且僅當(dāng)g為A1，BN，CN，D2K+2，E7，E8，F(xiàn)4和G2。事實(shí)證明，當(dāng)G的類型是DN與n個(gè)奇數(shù)，則Z(UQ(G))同構(gòu)與n + 1個(gè)變量和一個(gè)關(guān)系多項(xiàng)式代數(shù)的商代數(shù)，和而當(dāng)g為E6，那么Z( UQ(G))同構(gòu)于多項(xiàng)式代數(shù)與14個(gè)變量和八個(gè)關(guān)系商代數(shù)。

　　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.