Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra
(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:
https://lup.lub.lu.se/record/960024
- author
- de Jeu, Marcel ; Svensson, Christian and Silvestrov, Sergei LU
- organization
- publishing date
- 2007
- 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- unpublished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}}, }