The maximal solvable subgroups of SO(p,q) groups

A recursive procedure is developed that makes it possible to determine all conjugacy classes under both SO(p,q) and O(p,q) of the maximal solvable subalgebras of the Lie algebras LO(p,q) [and the continuous maximal solvable subgroups of SO(p,q)]. The cases of greatest physical interest with p ≥ q ≥ 0 and p + q ≤ 6 are considered in detail (they include the Lorentz group, de Sitter groups, and the conformal group of space-time). Formulas (in terms of Fibonacci numbers) are given for the number of O(p,q) [and SO(p,q)] equivalence classes of maximal solvable subalgebras of LO(p,q).