Analogs of Iu() and U(,1)
Feb, 199022 pages
Published in:
- J.Math.Phys. 32 (1991) 1227-1234
DOI:
Report number:
- EP-CPT-A952-0290
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Abstract: (AIP)
The starting point is the nonsemisimple, inhomogeneous Lie algebra U n ×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 U q (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 U q (U(n+1)) on a Gelfeld–Zetlin basis. Finally, the related construction of U q (U(n,1)) is presented and discussed. Here, U q (SU(1,1)), the q‐analog of relativistic motion in a plane, is analyzed in the context of this formalism.References(1)
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