Inequivalent sets of commuting missing label operators for the nuclear surfon model

WORKSHOP ON HIGHER SYMMETRIES IN PHYSICS 6–8 November 2008, Universidad Complutense de Madrid, Madrid, SpainWe exhibit a possible choice for the four available functionally independent labelling operators for the missing label problem associated to the reduction chain so(5) ⊃ so(3).Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems

Trace formulas for the Casimir operators of the unextended Schrödinger algebra S(N)

Using the contraction of the centrally extended Schrödinger algebrâS(N) onto the Lie algebra S(N) ⊕ R in combination with the Newton identities associated with the characteristic polynomial of a matrix, we derive explicit expressions for the Casimir operators of the unextended Schrödinger algebra S(N) in terms of trace operators. It is shown that these operators can be defined independently of the contraction from which a direct method for the computation of the S(N)-invariants is deduced