Twosided ideals in qdeformed Heisenberg algebras
(2005) In Expositiones Mathematicae 23(2). p.9999 Abstract
 In this article, the structure of twosided ideals in the qdeformed Heisenberg algebras defined by the qdeformed Heisenberg canonical commutation relation ABqBA=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 nontrivial twosided ideals, thus deducing by explicit construction that the qdeformed Heisenberg algebras are not just nonsimple but also nonartinian for q not equal 1, 0. We establish a connection between the quotients of the qdeformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in qdeformed Heisenberg algebras, investigate properties of deformed... (More)
 In this article, the structure of twosided ideals in the qdeformed Heisenberg algebras defined by the qdeformed Heisenberg canonical commutation relation ABqBA=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 nontrivial twosided ideals, thus deducing by explicit construction that the qdeformed Heisenberg algebras are not just nonsimple but also nonartinian for q not equal 1, 0. We establish a connection between the quotients of the qdeformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in qdeformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in qdeformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of qdeformed Heisenberg algebras. (Less)
Please use this url to cite or link to this publication:
http://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
 qdeformed Heisenberg algebras, twosided ideals
 in
 Expositiones Mathematicae
 volume
 23
 issue
 2
 pages
 99  99
 publisher
 Urban & Fischer Verlag
 external identifiers

 wos:000230029000001
 scopus:20844452572
 ISSN
 07230869
 DOI
 10.1016/j.exmath.2005.01.003
 language
 English
 LU publication?
 yes
 id
 eca64d19889648a09d9d46caa75391ff (old id 235757)
 date added to LUP
 20070928 09:20:49
 date last changed
 20180107 09:24:47
@article{eca64d19889648a09d9d46caa75391ff, abstract = {In this article, the structure of twosided ideals in the qdeformed Heisenberg algebras defined by the qdeformed Heisenberg canonical commutation relation ABqBA=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 nontrivial twosided ideals, thus deducing by explicit construction that the qdeformed Heisenberg algebras are not just nonsimple but also nonartinian for q not equal 1, 0. We establish a connection between the quotients of the qdeformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in qdeformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in qdeformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of qdeformed Heisenberg algebras.}, author = {Hellstrom, L and Silvestrov, Sergei}, issn = {07230869}, keyword = {qdeformed Heisenberg algebras,twosided ideals}, language = {eng}, number = {2}, pages = {9999}, publisher = {Urban & Fischer Verlag}, series = {Expositiones Mathematicae}, title = {Twosided ideals in qdeformed Heisenberg algebras}, url = {http://dx.doi.org/10.1016/j.exmath.2005.01.003}, volume = {23}, year = {2005}, }