Invariant Operators of Five-Dimensional Nonconjugate Subalgebras of the Lie Algebra of the Poincaré Group P(1,4)

Table 13

Invariant operators of subalgebras of the type 𝐴^𝑎𝑏_4,6⊕𝐴₁.

Basis elements of subalgebras	Invariant operators
𝑎=𝑒,𝑏=𝑒∶𝑋4,𝑃1,𝑃2,𝐿3+𝑒𝐺,𝑒>0⊕𝑋3	𝑋^24𝑃^21+𝑃^22, 𝑃^21+𝑃^22𝑃1+𝑖𝑃2𝑃1−𝑖𝑃2^𝑖𝑒, 𝑋3, 𝑒>0
𝑎=𝑒,𝑏=0∶𝑋4,𝑋1,𝑋2,𝐿3+𝑒𝐺,𝑒>0⊕𝑋3	𝑋^21+𝑋^22, ln𝑋4𝑋+𝑒arcsin^1𝑋^21+𝑋^22, 𝑋3, 𝑒>0