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

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

1996-01-02

arxiv.org/abs/q-alg/9601001v2

J.Phys.A29:3075-3088,1996; Addendum-ibid.A30:5239-5242,1997

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/29/12/015

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.

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