Nonstandard q-deformation of the Euclidean Lie algebra and its representations |
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Authors: | A U Klimyk |
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Institution: | (1) Institute for Theoretical Physics, Kiev, 252143, Ukraine. |
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Abstract: | A nonstandard q-deformed Euclidean algebra U
q(iso
n
), based on the definition of the twisted q-deformed algebra U
qson) (different from the Drinfeld–Jimbo algebra U
q(so
n
)), is defined. Infinite dimensional representations R of U
q(iso
n
) are described. Explicit formulas for operators of these representations in the orthonormal basis are given. The spectra of the operators R(T
n) corresponding to a q-analogue of the infinitesimal operator of shifts along the n-th axis are described. Contrary to the case of the classical Euclidean Lie algebra iso
n
, these spectra are discrete and spectral points have one point of accumulation. |
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Keywords: | |
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