On some nonlinear extensions of the angular momentum algebra

Details On some nonlinear extensions of the angular momentum algebra On some nonlinear extensions of the angular momentum algebra

1995-03-17

arxiv.org/abs/q-alg/9503009v1

J. Phys. A 28 (1995) 2847-2860

Mathematics

Quantum Algebra

22 pages, plain TeX + preprint.sty, no figures, to appear in J.Phys.A

Scientific paper

10.1088/0305-4470/28/10/015

Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the latter go over into those of the corresponding Lie algebras that contain each of the so(3) unitary irreducible representations at most once. It is also proved that similar deformations of the Lie algebras su(3), sl(3,R), and of the semidirect sum of an abelian algebra t(5) and so(3) do not lead to associative algebras.

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