Hidden symmetries in generalized su(2) algebras

We propose an algebraic formalism that contains the su(2) algebra as a part icular case. This generalization follows the same ideas recently developed to the Heisenberg algebra and allows a geometrical visualization of the eig envalues of the generator of the algebra, unveiling a hidden symmetry behin d the sequence of eigenvalues of this operator. A particular (linear) case is studied in detail providing finite-dimensional spin-x, representation fo r real alpha (j). More general situations (non-linear) could also be studie d, leading to a multi parametric deformation of the su(2) algebra. A connec tion with the formalism of dynamical systems is also exhibited and it is sh own how the representation theory of this algebra uses the concepts of attr actors and stability of attractors. (C) 2001 Elsevier Science B.V. All righ ts reserved.