On Nonlinear Angular Momentum Theories, Their Representations and Associated Hopf Structures

Abstract

Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear $sl(2)$-case as well as its $q$-deformation are easily recovered as specific examples. Two other physically interesting applications corresponding to the so-called Higgs and quadratic algebras are also considered. We show that these two nonlinear algebras can be equipped with a Hopf structure.

20 pages, Latex, Minor change, to be published in Jour. Phys. A: Math. Gen

References in corpus (2)

• Deformed oscillator algebras for two dimensional quantum superintegrable systems
• Generalized Deformed su(2) Algebras, Deformed Parafermionic Oscillators and Finite W Algebras

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