Connection between type B (or C) and F factorizations and construction of algebras
arXiv:math-ph/0112060 · doi:10.1088/0305-4470/35/12/310
Abstract
In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.
minor changes, 1 additional reference, final form to be published in JPA