Simple weight modules over the quantum Schrödinger algebra

Abstract

In the present paper, using the technique of localization, we determine the center of the quantum Schrödinger algebra ${\S }_q$ and classify simple modules with finite-dimensional weight spaces over ${\S }_q$, when $q$ is not a root of unity. It turns out that there are four classes of such modules: dense $U_q({\mathfrak{sl}}_2)$-modules, highest weight modules, lowest weight modules, and twisted modules of highest weight modules.

References in corpus (1)

• Quantized symplectic oscillator algebras of rank one