Advanced

Two-sided ideals in q-deformed Heisenberg algebras

Hellstrom, L and Silvestrov, Sergei LU (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:
author
organization
publishing date
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
2007-09-28 09:20:49
date last changed
2017-01-01 07:10:14
@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},
  keyword      = {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},
  volume       = {23},
  year         = {2005},
}