Algebraic Dependence of Commuting Elements in Algebras
(2009) International Workshop of BalticNordic Algebra, Geometry and Mathematical Physics p.265280 Abstract
 The aim of this paper to draw attention to several aspects of the algebraic dependence in algebras. The article starts with discussions of the algebraic dependence problem in commutative algebras. Then the BurchnallChaundy construction for proving algebraic dependence and obtaining the corresponding algebraic curves for commuting differential operators in the Heisenberg algebra is reviewed. Next some old and new results on algebraic dependence of commuting qdifference operators and elements in qdeformed Heisenberg algebras are reviewed. The main ideas and essence of two proofs of this are reviewed and compared. One is the algorithmic dimension growth existence proof. The other is the recent proof extending the BurchnallChaundy approach... (More)
 The aim of this paper to draw attention to several aspects of the algebraic dependence in algebras. The article starts with discussions of the algebraic dependence problem in commutative algebras. Then the BurchnallChaundy construction for proving algebraic dependence and obtaining the corresponding algebraic curves for commuting differential operators in the Heisenberg algebra is reviewed. Next some old and new results on algebraic dependence of commuting qdifference operators and elements in qdeformed Heisenberg algebras are reviewed. The main ideas and essence of two proofs of this are reviewed and compared. One is the algorithmic dimension growth existence proof. The other is the recent proof extending the BurchnallChaundy approach from differential operators and the Heisenberg algebra to the qdeformed Heisenberg algebra, showing that the BurchnallChaundy eliminant construction indeed provides annihilating curves for commuting elements in the qdeformed Heisenberg algebras for q not a root of unity. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2799095
 author
 Silvestrov, Sergei ^{LU} ; Svensson, Charlotte ^{LU} and de Jeu, M.
 organization
 publishing date
 2009
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 host publication
 Generalized Lie Theory in Mathematics, Physics and Beyond
 pages
 16 pages
 publisher
 Springer
 conference name
 International Workshop of BalticNordic Algebra, Geometry and Mathematical Physics
 conference location
 Lund Univ, Ctr Math Sci, Lund, Sweden
 conference dates
 20061012  20061014
 external identifiers

 wos:000264638600023
 scopus:58149162556
 ISBN
 9783540853312
 DOI
 10.1007/9783540853329_23
 language
 English
 LU publication?
 yes
 id
 0f9898d069854ef9bce1a07dbc69f0e7 (old id 2799095)
 date added to LUP
 20160404 11:25:41
 date last changed
 20210616 05:43:50
@inproceedings{0f9898d069854ef9bce1a07dbc69f0e7, abstract = {The aim of this paper to draw attention to several aspects of the algebraic dependence in algebras. The article starts with discussions of the algebraic dependence problem in commutative algebras. Then the BurchnallChaundy construction for proving algebraic dependence and obtaining the corresponding algebraic curves for commuting differential operators in the Heisenberg algebra is reviewed. Next some old and new results on algebraic dependence of commuting qdifference operators and elements in qdeformed Heisenberg algebras are reviewed. The main ideas and essence of two proofs of this are reviewed and compared. One is the algorithmic dimension growth existence proof. The other is the recent proof extending the BurchnallChaundy approach from differential operators and the Heisenberg algebra to the qdeformed Heisenberg algebra, showing that the BurchnallChaundy eliminant construction indeed provides annihilating curves for commuting elements in the qdeformed Heisenberg algebras for q not a root of unity.}, author = {Silvestrov, Sergei and Svensson, Charlotte and de Jeu, M.}, booktitle = {Generalized Lie Theory in Mathematics, Physics and Beyond}, isbn = {9783540853312}, language = {eng}, pages = {265280}, publisher = {Springer}, title = {Algebraic Dependence of Commuting Elements in Algebras}, url = {http://dx.doi.org/10.1007/9783540853329_23}, doi = {10.1007/9783540853329_23}, year = {2009}, }