Comment on ``Generalized $q$-oscillators and their Hopf structures''

Details Comment on ``Generalized $q$-oscillators and their Hopf structures'' Comment on ``Generalized $q$-oscillators and their Hopf structures''

1995-10-02

arxiv.org/abs/q-alg/9510001v1

J. Phys. A 28 (1995) 7019-7025

Mathematics

Quantum Algebra

9 pages, LaTeX, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/28/23/039

In a recent paper (1994 {\sl J.\ Phys.\ A: Math.\ Gen.\ }{\bf 27} 5907), Oh and Singh determined a Hopf structure for a generalized $q$-oscillator algebra. We prove that under some general assumptions, the latter is, apart from some algebras isomorphic to su$_q$(2), su$_q$(1,1), or their undeformed counterparts, the only generalized deformed oscillator algebra that supports a Hopf structure. We show in addition that the latter can be equipped with a universal $\cR$-matrix, thereby making it into a quasitriangular Hopf algebra.

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