Abstract
A new q-deformed Euclidean algebra Uq(ison), based on a definition of the algebra Uq(son) different from the Drinfeld-Jimbo definition, is given. Infinite-dimensional representations Ta of this algebra, characterized by one complex number, is described. Explicit formulas for operators of these representations in an orthonormal basis are derived. The spectrum of the operator Ta(In) corresponding to a q-analogue of the infinitesimal operator of shifts along the n-th axis is given. Contrary to the case of the classical Euclidean algebraison, this spectrum is discrete and the spectrum points have one point of accumulation.
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