**The International Conference on
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Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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Reduced system of Bethe equations for three-boson interaction

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V.A. Andreev, O.A. Ivanova

Lebedev Physical Institute, Optical Department, Leninsky Prospect 53, 117924 Moscow, Russia M. V. Lomonosov Moscow State University, Department of Mechanics and Mathematics, 119899, Moscow, Russia

**Abstract:** The reduced system of Bethe equations is found for three-boson interaction. The invariants and surfaces in the space of Bethe parameters, connected with this system, are constructed. It is shown that at these surfaces the eigenvectors can be presented in power form. Connection between Bethe ansatz and polynomial extensions of Lie algebras is briefly discussed. The computational procedures corresponding to the original Bethe equations and the method of polynomial algebras are compared.

**Keywords:** Bethe ansatz, eigenvector, invariant, surface, polynomial algebra

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