Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
32 (1991), S. 1227-1234
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The starting point is the nonsemisimple, inhomogeneous Lie algebra Un×I2n [denoted also as IU(n)], where I2n represents an Abelian subalgebra in semidirect product with the homogeneous part U(n). This is realized by explicitly giving the matrix elements of the generators on a modified Gelfand–Zetlin basis that allows representations of infinite dimensions. The enveloping algebra is q lifted by introducing q brackets in the matrix elements giving Uq(IU(n)). The deformation of the Abelian structure of I2n is studied for q≠1. Some implications are pointed out. The important invariants are constructed for arbitrary n. The results are compared to the corresponding ones for Jimbo's construction of Uq (U(n+1)) on a Gelfeld–Zetlin basis. Finally, the related construction of Uq(U(n,1)) is presented and discussed. Here, Uq(SU(1,1)), the q-analog of relativistic motion in a plane, is analyzed in the context of this formalism.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529319
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