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Algebraic curves for commuting elements in the q-deformed Heisenberg algebra

de Jeu, M.; Svensson, Charlotte LU and Silvestrov, Sergei LU (2009) In Journal of Algebra 321(4). p.1239-1255
Abstract
In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series. (C) 2008 Elsevier Inc. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
q-Deformed Heisenberg algebra, Commuting elements, Algebraic dependence, Eliminant, DIFFERENCE OPERATORS
in
Journal of Algebra
volume
321
issue
4
pages
1239 - 1255
publisher
Elsevier
external identifiers
  • wos:000263333400008
  • scopus:58149157792
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2008.10.021
language
English
LU publication?
yes
id
268dd18d-e67d-4d3f-ab1b-ea7f9e301029 (old id 2799124)
date added to LUP
2012-06-19 11:34:25
date last changed
2017-12-10 03:52:39
@article{268dd18d-e67d-4d3f-ab1b-ea7f9e301029,
  abstract     = {In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series. (C) 2008 Elsevier Inc. All rights reserved.},
  author       = {de Jeu, M. and Svensson, Charlotte and Silvestrov, Sergei},
  issn         = {0021-8693},
  keyword      = {q-Deformed Heisenberg algebra,Commuting elements,Algebraic dependence,Eliminant,DIFFERENCE OPERATORS},
  language     = {eng},
  number       = {4},
  pages        = {1239--1255},
  publisher    = {Elsevier},
  series       = {Journal of Algebra},
  title        = {Algebraic curves for commuting elements in the q-deformed Heisenberg algebra},
  url          = {http://dx.doi.org/10.1016/j.jalgebra.2008.10.021},
  volume       = {321},
  year         = {2009},
}