Hidden symmetries in generalized su(2) algebras

We propose an algebraic formalism that contains the su(2) algebra as a particular case. This generalization follows the same ideas recently developed to the Heisenberg algebra and allows a geometrical visualization of the eigenvalues of the generator of the algebra, unveiling a hidden symmetry behind the sequence of eigenvalues of this operator. A particular (linear) case is studied in detail providing finite-dimensional spin-αj representation for real αj. More general situations (non-linear) could also be studied, leading to a multi parametric deformation of the su(2) algebra. A connection with the formalism of dynamical systems is also exhibited and it is shown how the representation theory of this algebra uses the concepts of attractors and stability of attractors