Real Forms of the Oscillator Quantum Algebra and its Representations

Abstract

We consider the conditions under which the $q$-oscillator algebra becomes a Hopf $\ast$-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.

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

Cited by in corpus (1)

• Some comments on $q$-deformed oscillators and $q$-deformed $su(2)$ algebras