  A ladder algebraic structure for $L^2(\mathbb{R}^+)$ which closes the Lie
algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is
presented in terms of a basis of associated Laguerre polynomials. Using the
Schwinger method the quadratic generators that span the alternative Lie
algebras $so(3)$, $so(2,1)$ and $so(3,2)$ are also constructed. These families
of (pseudo) orthogonal algebras also allow to obtain unitary irreducible
representations in $L^2(\mathbb{R}^2)$ similar to those of the spherical
harmonics.
