Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 19.5.2009 |
| Speaker: | Severin Pošta, FJFI, České vysoké učení technické v Praze |
| Title: | Center of the nonstandard quantum deformation $U_q'(so_3)$ |
| Abstract: | The center of the universal enveloping algebra of a semi simple Lie algebra is a free polynomial algebra. It can be described quite explicitly with the help of Harish-Chandra homomorphism. This situation is preserved when we move to the quantum case and deformation parameter is not root of unity. For the example, in the simplest case of the algebra $U_q(sl_2)$, the center is generated by $Cq$, where $Cq$ denotes deformed Casimir element. When $q$ is root of unity, the situation is much more difficult. Center is typically much larger and the central elements satisfy nontrivial polynomial relations. We show this is also the case when we consider nonstandard Fairlie-Klimyk deformation $U_q'(so_3)$. |
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