Abstract
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 su q1/2(2) with different conjugations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Faddeev, L. D., Les Houches Lectures 1982, Elsevier, Amsterdam, 1984. Kulish, P. P. and Sklyanin, E. K., Lecture Notes in Physics 151, Springer, Berlin, 1982.
Yang, C. N., Phys. Rev. Lett. 19 1312 (1967); Baxter, R. J., Exactly Solved Models in Statistical Mechanics, Academic, New York, 1982.
Zamolodchikov, A. and Zamolodchikov, Ab., Ann. Phys. 120, 252 (1979); de Vega, H., Internat. J. Modern Phys. 4, 2371 (1989).
Moore, G. and Seiberg, N., Nuclear Phys. B 313, 16 (1989), Comm. Math. Phys. 123, 177 (1989).
Drinfeld, V. G., Proc. Internat. Congr. Math., Berkeley, Vol. 1, 1986, p. 798.
Macfarlane, A. J., J. Phys. A. 22, 4581 (1989).
Biedenharn, L. C., J. Phys. A 22, L873 (1989).
Yan, H., J. Phys. A 23, L1155 (1990).
Floreanini, R. and Vinet, L., Lett. Math. Phys. 22, 45 (1991).
Masuda, T., Mimachi, K., Nakagami, Y., Noumi, M., Saburi, Y., and Ueno, K., Lett. Math. Phys. 19, 187 (1990).
Lukierski, J., Nowicki, A., and Reugg, H., Phys. Lett. B 271 321 (1991).
Fröhlich, J. and Kerler, T., Lecture Notes in Mathematics 1542, Springer-Verlag, Berlin, 1993.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oh, C.H., Singh, K. Real forms of the oscillator quantum algebra and its representations. Lett Math Phys 36, 77–85 (1996). https://doi.org/10.1007/BF00403253
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00403253