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Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra

de Jeu, Marcel; Svensson, Christian and Silvestrov, Sergei LU (2007) In Preprints in Mathematical Sciences1999-01-01+01:00
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
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
q-deformed Heisenberg algebra, commuting elements, Burchnall-Chaundy eliminant construction, algebraic dependence
in
Preprints in Mathematical Sciences1999-01-01+01:00
issue
23
pages
17 pages
publisher
Lund University
external identifiers
  • Other:LUTFMA-5089-2007/1-17/(2007)
ISSN
1403-9338
project
Non-commutative Geometry in Mathematics and Physics
Non-commutative Analysis of Dynamics, Fractals and Wavelets
language
English
LU publication?
yes
id
6e679837-0e32-4a5c-a277-65218bbf126f (old id 960024)
alternative location
http://arxiv.org/abs/0710.2748
date added to LUP
2008-01-28 14:49:38
date last changed
2016-11-25 14:42:38
@misc{6e679837-0e32-4a5c-a277-65218bbf126f,
  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},
  author       = {de Jeu, Marcel and Svensson, Christian and Silvestrov, Sergei},
  issn         = {1403-9338},
  keyword      = {q-deformed Heisenberg algebra,commuting elements,Burchnall-Chaundy eliminant construction,algebraic dependence},
  language     = {eng},
  number       = {23},
  pages        = {17},
  publisher    = {ARRAY(0x8635298)},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra},
  year         = {2007},
}