Coordinates of the quantum plane as q-tensor operators in U{sub q} (su(2) * su(2))
- Univ. of Texas, Austin, TX (United States)
The relation between the set of transformations M{sub q}(2) of the quantum plane and the quantum universal enveloping algebra U{sub q}(u(2)) is investigated by constructing representations of the factor algebra U{sub q} (u(2) * u(2)). The non-commuting coordinates of M{sub q}(2), on which U{sub q}(2) * U{sub q}(2) acts, are realized as q-spinors with respect to each U{sub q}(u(2)) algebra. The representation matrices of U{sub q}(2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of M{sub q}(2) directly from properties of U{sub q}(u(2)). The generalization of these results to U{sub q}(u(n)) and M{sub q}(n) is also discussed.
- Research Organization:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG03-93ER40757
- OSTI ID:
- 28358
- Report Number(s):
- DOE/ER/40757-058; ON: DE95007100; IN: CPP-94-35; TRN: 95:008280
- Resource Relation:
- Other Information: PBD: 13 Jan 1995
- Country of Publication:
- United States
- Language:
- English
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