Abstract
A nonstandard q-deformed Euclidean algebra Uq(ison), based on the definition of the twisted q-deformed algebra Uqson) (different from the Drinfeld–Jimbo algebra Uq(son)), is defined. Infinite dimensional representations R of Uq(ison) are described. Explicit formulas for operators of these representations in the orthonormal basis are given. The spectra of the operators R(Tn) 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 ison, these spectra are discrete and spectral points have one point of accumulation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
