Abstract
New Lie-algebraic structures (polynomial deformations of Lie algebras) are revealed in some problems of quantum optics and laser physics. Specifically, deformations of oscillator algebras due to extensions of unitary algebras by their symmetric and skew-symmetric tensors are shown to be algebras of dynamic symmetry (ADS) in models of n-photon processes with internal symmetries. Similarly, deformed algebras sud(2) are found as ADS in the context of generalized Dicke models and frequency conversion models. We also briefly discuss some possible schemes of employing the results to solving physical problems.
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