Superintegrable systems in two-dimensional (2D) Darboux spaces were classified and it
was found that there exist 12 distinct classes of superintegrable systems with quadratic …

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central
terms. We find a novel underlying chain structure of quadratic algebras formed by the …

In this paper we show that the chain structure of (overlapping) quadratic algebras, recently
introduced in Liao et al (2018 J. Phys. A: Math. Theor. 51 255201) in the analysis of the nD …

We introduce a new superintegrable Kepler–Coulomb system with non-central terms in N-
dimensional Euclidean space. We show this system is multiseparable and allows separation …

Finite and Infinite-dimensional representations of symmetry algebras play a significant role
in determining the spectral properties of physical Hamiltonians. In this paper, we introduce …

By applying the recurrence approach and coupling constant metamorphosis, we construct
higher order integrals of motion for the Stackel equivalents of the N-dimensional …

We extend the method for constructing symmetry operators of higher order for two-
dimensional quantum Hamiltonians by Kalnins et al (2010 J. Phys. A: Math. Theor. 43 …

The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres -
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We propose a systematic procedure to construct polynomial algebras from intermediate
Casimir invariants arising from (semisimple or non-semisimple) Lie algebras $\mathfrak {g} …

In recent years, various nonlinear algebraic structures have been obtained in the context of
quantum systems as symmetry algebras, Painlevé transcendent models, and missing label …