Graded contractions of symplectic Lie algebras in collective models (Q2785765)

The symplectic Lie algebras \(sp(2,\mathbb{C})\), \(sp(2,\mathbb{R})\), \(sp(3,\mathbb{C})\), \(sp(3,\mathbb{R})\) admit a \(\mathbb{Z}_2\times \mathbb{Z}_2\)-grading induced by time reversal and the exchange of coordinates and momenta. Therefore, all \(\mathbb{Z}_2\times \mathbb{Z}_2\)-graded contractions can be written down, in this paper it is the subset which preserves space isotropy. Some of the resulting Lie algebras are used in physics (e.g. nuclear collective model, model of an affinely rigid body).