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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 Sciences
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
; and
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unpublished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 Sciences
issue
23
pages
17 pages
publisher
Lund University
external identifiers
  • other:LUTFMA-5089-2007/1-17/(2007)
ISSN
1403-9338
project
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
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
2016-04-04 09:11:59
date last changed
2018-11-21 20:51:26
@article{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}},
  keywords     = {{q-deformed Heisenberg algebra; commuting elements; Burchnall-Chaundy eliminant construction; algebraic dependence}},
  language     = {{eng}},
  number       = {{23}},
  publisher    = {{Lund University}},
  series       = {{Preprints in Mathematical Sciences}},
  title        = {{Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra}},
  url          = {{http://arxiv.org/abs/0710.2748}},
  year         = {{2007}},
}