Abstract
In this paper we present a method of construction of the basis vectors of the hierarchy of algebras. Furthermore, a procedure for an efficient calculation of the matrix elements is developed. The method applied for the calculation of the energy eigenvalues and eigenstates for the case of a linear ring of sixteen spins with nearest-neighbor and next-nearest-neighbor interactions. The numerical results for the nearest-neighbor interaction are compared with those already calculated by other authors and are found to coincide.
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