Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 5.10.2007 |
| Speaker: | Čestmír Burdík, FJFI, České vysoké učení technické |
| Title: | The adjoint representation of quantum algebra $U_q(\mathrm{sl}(2))$ |
| Abstract: | (spoluautoři: O. Navrátil and S. Pošta) Starting from any representation of the Lie algebra g on the infinite dimensional vector space $V$ we can construct the representation on space $\mathrm{Aut}(V)$. These representations are of the type ad. That is one of the reason, why it is important to study the adjoint representation of the Lie algebra ${\mathfrak g}$ on the universal enveloping algebra $U({\mathfrak g})$. A similar situation is for the quantum groups $U_q({\mathfrak g})$. In this paper we study the adjoint representation for the simplest quantum algebra $U_q(\mathrm{sl}(2))$ in the case that $q$ is not a root of unity. |
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