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### 2019年度数学科第３回談話会のお知らせ / 開催日：令和元年８月２３日（金）

2019年8月8日

令和元年８月２３日（金）に、2019年度数学科第３回談話会を下記のとおり開催いたします。

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 日　時 ２０１９年８月２３日（金） 　１４：００～１５：００ 場　所 富山大学理学部 B 棟 1 階　B121室 講演者 Libin Li氏 （Department of Mathematics, Yangzhou University, China）
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The center subalgebra of the quantized enveloping algebra of a finite dimensional simple Lie algebra

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

The results reported here are based on the joint work with Limeng Xia and Yinhuo Zhang.