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  • 天元讲堂(6.1): On the center of the quantized enveloping algebra of a simple Lie algebra
  • 浏览量:257 发布人:佚名 发布时间:2017-05-26 11:14:28
  • 报告人: 夏利猛教授(江苏大学)

    报告时间:6月1日 上午 10:00-11:00

    报告地点: 维格堂119

    摘要: Let $\sg$ be a  finite dimensional simple complex Lie algebra and $U=U_q(\sg)$ the quantized enveloping algebra (in the sense of Jantzen) with $q$ being generic. In this paper, we show that the center $Z(U_q(\sg))$ of the quantum group $U_q(\sg)$ is isomorphic to a monoid algebra, and  that $Z(U_q(\sg))$ is a polynomial algebra if and only if $\sg$ is of  type $A_1, B_n, C_n, D_{2k+2}, E_7, E_8, F_4$  or $G_2.$  Moreover,  in case $\sg$ is of type $D_{n}$ with $n$ odd,  then $Z(U_q(\sg))$ is isomorphic to a quotient algebra of a polynomial algebra in $n+1$ variables  with one relation;  in case $\sg$ is of type $E_6$,  then $Z(U_q(\sg))$ is isomorphic to a quotient algebra of a polynomial algebra in fourteen variables with eight relations;  in case $\sg$ is of type $A_{n}$, then $Z(U_q(\sg))$ is isomorphic to a quotient algebra of a polynomial algebra described by $n$-sequences.

     

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