Beyond fuzzy spheres

Understand

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra.

• We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$.
• We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level.
• Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra.