Noncommutative dynamical models with quantum symmetries
The authors study the \(q\)-Minkowski space algebra \(\mathcal{L}(q)\) (which is a deformation of the coordinate algebra \(\mathbb{K}[gl(n)^*]\)) and its ``sl-reduction''. Their aim is to deform some dynamical models with usual symmetries into models with quantum symmetries and to find their integrals. The authors construct a family of Verma modules over both \(\mathcal{L}(q)\) and the corresponding sl-reduction, and endow both the algebras in question and the corresponding Verma modules with a \(U_q(sl(2))\)-action. Further, the authors define some dynamical models on both \(\mathcal{L}(q)\) and the corresponding sl-reduction. In particular, they introduce a \(q\)-analogue of the Runge-Lenz vector and, finally, quantize the dynamics in space-time with a spherically symmetric metric.
scientific article; zbMATH DE number 5319027