Non-linear generalization of the sl(2) algebra

Details Non-linear generalization of the sl(2) algebra Non-linear generalization of the sl(2) algebra

2002-07-29

arxiv.org/abs/math-ph/0207045v1

Phys.Lett. A300 (2002) 205-212

Physics

Mathematical Physics

13 pages, 3 EPS figures, Latex

Scientific paper

10.1016/S0375-9601(02)00820-4

We present a generalization of the sl(2) algebra where the algebraic relations are constructed with the help of a general function of one of the generators. When this function is linear this algebra is a deformed sl(2) algebra. In the non-linear case, the finite dimensional representations are constructed in two different ways. In the first case, which provides finite dimensional representations only for the non-linear case, these representations come from solutions to a dynamical equation and we show how to construct explicitly these representations for a general quadratic non-linear function. The other type of finite dimensional representation comes from solutions to a cut condition equation. We give examples of solutions of this type in the non-linear case as well.

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