Deformations of Mathematical Structures II pp 155-160 | Cite as
Operator Realisations of Quantum Heisenberg-Weyl and SU(2)q algebras
Chapter
Abstract
The quantum-deformed Heisenberg-Weyl algebra H q and its representations are investigated. The explicit realisations of this q-deformed algebra are founded. A realisation of SU(2) q quantum group with help of only one pair of the bosonic creation and annihilation operators is obtained. Two different cases are discussed: with the use of the q-deformed and the standard Heisenberg-Weyl algebra. Finally a realisation of SU(2) q algebra in the Woronowicz sense is given.
Preview
Unable to display preview. Download preview PDF.
References
- [1]Drinfeld, V.G.: 1988, Sov. Math. Dokl. 36, 212.MathSciNetGoogle Scholar
- [2]Sklynian, E.K.: 1982, Funct. Anal. Appl. 16, 262.Google Scholar
- [3]Kulish, P.P., Reshetikhin, N.Y.: 1983, J. Sov. Math. 23, 2435.CrossRefGoogle Scholar
- [4]Jimbo, M.: 1985, Lett. Math. Phys. 10, 63; 1986, Commun. Math. Phys. 102, 537.MathSciNetGoogle Scholar
- [5]Woronowicz, S.: 1987, Commun. Math. Phys. 111, 613.MathSciNetMATHCrossRefGoogle Scholar
- [6]Kirillov, A.N., Reshetikhin, N.Y.: 1988, preprint LOMI E-9–88.Google Scholar
- [7]Biedenharn, L.C.: 1989, J. Phys. A: Math. Gen. 22, L873.MathSciNetMATHCrossRefGoogle Scholar
- [8]Macfarlane, A.J.: 1989, J. Phys. A: Math. Gen. 22, 4581.MathSciNetMATHCrossRefGoogle Scholar
- [9]Sun, C-P., Fu, H-C.: 1989, J. Phys. A: Math. Gen. 22, L983.MathSciNetMATHCrossRefGoogle Scholar
- [10]Biedenharn, L.C., Cusson, R.Y., Han M.Y., Weaver, O.L.: 1972, Phys. Lett. 42B, 257.Google Scholar
- [11]Bargmann, V.: 1961, Comm. Pure Appl. Math. 14, 187.MathSciNetMATHCrossRefGoogle Scholar
Copyright information
© Springer Science+Business Media Dordrecht 1994