On the Center of the Quantized Enveloping Algebra of A Semisimple Lie Algebra-University of Science and Technology of China

On the Center of the Quantized Enveloping Algebra of A Semisimple Lie Algebra

Date：2016-04-12

Speaker: XIA Limeng

Time: 2016-04-15, 16:00-17:30

Place: Room 1218, School of Mathematical Sciences

Detail：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.

Organizer: School of Mathematical Sciences