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

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Abstract
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).

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