Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2799124
- author
- de Jeu, M. ; Svensson, Charlotte LU and Silvestrov, Sergei LU
- organization
- publishing date
- 2009
- 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
- 2016-04-01 12:23:56
- date last changed
- 2022-01-27 03:10:56
@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}}, keywords = {{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}}, doi = {{10.1016/j.jalgebra.2008.10.021}}, volume = {{321}}, year = {{2009}}, }