Home > Papers

 
 
On the center of the quantized enveloping algebra of a semisimple Lie algebra
Li-bin Li 1 *,Li-meng Xia 2 *, Yin-huo Zhang 3
1. College of Mathematical Science, Yangzhou University, Yangzhou, 225009, China
2. Department of Mathematics, Jiangsu University, Zhenjiang, 212013, China
3. Department of Mathematics and Statistics, University of Hasselt, Universitaire Campus, 3590 Diepeenbeek, Belgium
*Correspondence author
#Submitted by
Subject:
Funding: Ph. D. Programs Foundation of Higher Education of China （No.20123250110005）
Opened online:31 May 2016
Accepted by: none
Citation: Li-bin Li,Li-meng Xia, Yin-huo Zhang.On the center of the quantized enveloping algebra of a semisimple Lie algebra[OL]. [31 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693188
 
 
Let $sg$ be a complex simple finite dimensional Lie algebra and $U=U_q(sg)$ the quantized enveloping algebra in Jantzen's sense with $q$ being generic. In this paper, we prove that the center $Z(U_q(sg))$ of the quantum group $U_{q}(sg)$ is isomorphic to a monoid algebra, and $Z(U_q(sg))$ is a polynomial algebra if and only if $sg$ is of type $A_1, B_n, C_n, D_{2k+2}, E_7, E_8, F_4$ and $G_2.$ It turns out that when $sg$ is of type $D_{n}$ with $n$ odd then $Z(U_q(sg))$ is isomorphic to a quotient algebra of polynomial algebra with $n+1$ variables and one relation, and while when $sg$ is of type $E_6$ then $Z(U_q(sg))$ is isomorphic to a quotient algebra of polynomial algebra with fourteen variables and eight relations.
Keywords:Center, Lie algebra, quantum group, Generators, generating relations
 
 
 

For this paper
  • ● PDF (0B)
  • ● Revision 0 　　
  • ● Print this paper
  • ● Recommend this paper to a friend
  • ● Add to my favorite list

    Saved Papers

    Please enter a name for this paper to be shown in your personalized Saved Papers list

Tags
Add yours

Related Papers

Statistics
PDF Downloaded 38
Bookmarked 0
Recommend 0
Comments Array
Submit your papers