Abstract
In this article, the structure of two-sided ideals in the q -deformed Heisenberg algebras defined by the q -deformed Heisenberg canonical commutation relation AB - qBA = I is investigated. We show that these algebras are simple if and only if q = 1 . For q ≠ 1 , 0 we present an infinite descending chain of non-trivial two-sided ideals, thus deducing by explicit construction that the q -deformed Heisenberg algebras are not just non-simple but also non-artinian for q ≠ 1 , 0 . We establish a connection between the quotients of the q -deformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in q -deformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in q -deformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of q -deformed Heisenberg algebras.
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.
