Abstract
A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0,P±] = ± P±, [P+,P-] = ϕ(m)(P0) where ϕ(m) (P0) is an m th order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l+m+1)th order polynomial algebras. This procedure follows from a generalization of the well-known Jordan–Schwinger method of construction of su(2) and su(1,1) algebras from two mutually commuting boson algebras.
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