Real Forms of the Oscillator Quantum Algebra and its Representations

Details Real Forms of the Oscillator Quantum Algebra and its Representations Real Forms of the Oscillator Quantum Algebra and its Representations

1995-08-24

arxiv.org/abs/q-alg/9508015v4

Mathematics

Quantum Algebra

10 pages, Ams-Tex, To be published in Letters in Mathematical physics

Scientific paper

10.1007/BF00403253

We consider the conditions under which the $q$-oscillator algebra becomes a
Hopf $*$-algebra. In particular, we show that there are at least two real forms
associated with the algebra. Furthermore, through the representations, it is
shown that they are related to ${\text {su}}_{q^{1/2}}(2)$ with different
conjugations.

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