Two-sided ideals in q-deformed Heisenberg algebras
(2005) In Expositiones Mathematicae 23(2). p.99-99- 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 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/235757
- author
- Hellstrom, L and Silvestrov, Sergei LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- q-deformed Heisenberg algebras, two-sided ideals
- in
- Expositiones Mathematicae
- volume
- 23
- issue
- 2
- pages
- 99 - 99
- publisher
- Urban & Fischer Verlag
- external identifiers
-
- wos:000230029000001
- scopus:20844452572
- ISSN
- 0723-0869
- DOI
- 10.1016/j.exmath.2005.01.003
- language
- English
- LU publication?
- yes
- id
- eca64d19-8896-48a0-9d9d-46caa75391ff (old id 235757)
- date added to LUP
- 2016-04-01 16:37:10
- date last changed
- 2022-01-28 20:55:58
@article{eca64d19-8896-48a0-9d9d-46caa75391ff,
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 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.}},
author = {{Hellstrom, L and Silvestrov, Sergei}},
issn = {{0723-0869}},
keywords = {{q-deformed Heisenberg algebras; two-sided ideals}},
language = {{eng}},
number = {{2}},
pages = {{99--99}},
publisher = {{Urban & Fischer Verlag}},
series = {{Expositiones Mathematicae}},
title = {{Two-sided ideals in q-deformed Heisenberg algebras}},
url = {{http://dx.doi.org/10.1016/j.exmath.2005.01.003}},
doi = {{10.1016/j.exmath.2005.01.003}},
volume = {{23}},
year = {{2005}},
}