SPIN-HAMILTONIANS BY MEANS OF HIERARCHIES OF GROUP-INDEXED ALGEBRAS .1. THE HIERARCHY OF ALGEBRAS

Many spin systems present high symmetries. That also is the case for t he isotropic Heisenberg Hamiltonian where both translational and rotat ional symmetries are present. A group theoretic analysis of the proble m leads to a hierarchy of algebras by means of which part of the Hamil tonian can be directly diagonalized, the rest being left for perturbat ion treatment. Many terms of the Hamiltonian represent mutually commut ing Casimir operators of the hierarchy of algebras.