Abstract
We stress the connection between [Formula: see text]-algebras and noncanonical Heisenberg algebras. We prove that the known Heisenberg–Weyl algebras for the deformed harmonic oscillators are partial cases of the Lie-admissible [Formula: see text]-algebras. We also point out the existence of a scale factor which plays an important role for the eigenvalue spectrum and for the generalized uncertainty Heisenberg relation. This factor has the form (Δx)(Δp) ≥ ℏ′/2 with ℏ′ = ℏκ and κ > 0.
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