Coordinates of the quantum plane asq-tensor operators in((mathfrak{s}mathfrak{u}(2)*mathfrak{s}mathfrak{u}(2)))

✍ Scribed by L. C. Biedenharn; M. A. Lohe

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 658 KB
• Volume: 36
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00403254

✦ Synopsis

The relation between the set of transformations ~02q(2) of the quantum plane and the quantum universal enveloping algebra q/q(u(2)) is investigated by constructing representations of the factor algebra ~'~(u(2) * u( 2)). The noncommuting coordinates of ~0/q(2), on which Uq(2)* Uq(2) acts, are realized as q-spinors with respect to each q/~(u(2)) algebra. The representatxon matrices of ok'q(2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of 9J/q(2) directly from properties of ~'q(u(2)). The generahzation of these results to Jk'q(u(n)) and 9.1/q(n) is also discussed.