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oai:uvadoc.uva.es:10324/814372026-03-20T08:27:48Zcom_10324_1159com_10324_931com_10324_894col_10324_1310

Kuru, Şengül Marquette, I Negro Vadillo, Francisco Javier 2026-01-13T15:57:08Z 2026-01-13T15:57:08Z 2020 J. Phys. A: Math. Theor. 53 (2020) 405203 (10pp) 1751-8113 https://uvadoc.uva.es/handle/10324/81437 10.1088/1751-8121/abadb7 405203 40 Journal of Physics A: Mathematical and Theoretical 53 1751-8121 We characterize the symmetry algebra of the generic superintegrable system on a pseudo-sphere corresponding to the homogeneous space SO(p, q + 1) /SO(p, q) where p+ q = N,N ∈N. These symmetries occur both in quantum as well as in classical systems in various contexts, so they are quite important in physics.We show that this algebra is independent of the signature (p, q + 1) of the metric and that it is the same as the Racah algebraR(N + 1). The spectrum obtained from R(N + 1) via the Daskaloyannis method depends on undetermined signs that can be associated to the signatures. Two examples are worked out explicitly for the cases SO(2, 1)/SO(2) and SO(3)/SO(2) where it is shown that their spectrum obtained by means of separation of variables coincide with particular choices of the signs, corresponding to the specific signatures, of the spectrum for the symmetry algebra R(3). Junta de Castilla y Le´on, Spain (BU229P18,VA137G18). I. Marquette was supported by Australian Research Council with a Future Fellowship FT180100099. application/pdf spa IOP publishing info:eu-repo/semantics/openAccess The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion SI