| Title | Two-sided ideals in q-deformed Heisenberg algebras |
| Authors | L Hellstrom, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Expositiones Mathematicae |
| Year | 2005 |
| Volume | 23 |
| Issue | 2 |
| Pages | 99 - + |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Urban & Fischer Verlag |
| Abstract English | 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 not equal 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 not equal 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. |
| Keywords | q-deformed Heisenberg algebras, two-sided ideals, |
| ISBN/ISSN/Other | ISSN: 0723-0869 |
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