On algebraic curves for commuting elements in $q$Heisenberg algebras
(2009) In Journal of Generalized Lie Theory and Applications 3(4). p.321328 Abstract
 In the present article we continue investigating the algebraic dependence of commuting
elements in qdeformed Heisenberg algebras. We provide a simple proof that the
0chain subalgebra is a maximal commutative subalgebra when q is of free type and that
it coincides with the centralizer (commutant) of any one of its elements dierent from
the scalar multiples of the unity. We review the BurchnallChaundytype construction for
proving algebraic dependence and obtaining corresponding algebraic curves for commuting
elements in the qdeformed Heisenberg algebra by computing a certain determinant
with entries depending on two commuting variables and one of the generators. The... (More)  In the present article we continue investigating the algebraic dependence of commuting
elements in qdeformed Heisenberg algebras. We provide a simple proof that the
0chain subalgebra is a maximal commutative subalgebra when q is of free type and that
it coincides with the centralizer (commutant) of any one of its elements dierent from
the scalar multiples of the unity. We review the BurchnallChaundytype construction for
proving algebraic dependence and obtaining corresponding algebraic curves for commuting
elements in the qdeformed Heisenberg algebra by computing a certain determinant
with entries depending on two commuting variables and one of the generators. The coe
cients in front of the powers of the generator in the expansion of the determinant are
polynomials in the two variables dening some algebraic curves and annihilating the two
commuting elements. We show that for the elements from the 0chain subalgebra exactly
one algebraic curve arises in the expansion of the determinant. Finally, we present several
examples of computation of such algebraic curves and also make some observations on
the properties of these curves. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2440747
 author
 Richter, Johan ^{LU} and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 BurchnallChaundy theory, Heisenberg algebra
 in
 Journal of Generalized Lie Theory and Applications
 volume
 3
 issue
 4
 pages
 321  328
 publisher
 Ashdin Publishing
 external identifiers

 scopus:84858232830
 ISSN
 17365279
 language
 English
 LU publication?
 yes
 id
 a6b5aeb43b8d4880b845daabfe365f85 (old id 2440747)
 alternative location
 http://www.ashdin.com/journals/jglta/2009/4/v3_n4_5.pdf
 date added to LUP
 20120831 15:57:29
 date last changed
 20180107 05:58:02
@article{a6b5aeb43b8d4880b845daabfe365f85, abstract = {In the present article we continue investigating the algebraic dependence of commuting<br/><br> elements in qdeformed Heisenberg algebras. We provide a simple proof that the<br/><br> 0chain subalgebra is a maximal commutative subalgebra when q is of free type and that<br/><br> it coincides with the centralizer (commutant) of any one of its elements dierent from<br/><br> the scalar multiples of the unity. We review the BurchnallChaundytype construction for<br/><br> proving algebraic dependence and obtaining corresponding algebraic curves for commuting<br/><br> elements in the qdeformed Heisenberg algebra by computing a certain determinant<br/><br> with entries depending on two commuting variables and one of the generators. The coe<br/><br> cients in front of the powers of the generator in the expansion of the determinant are<br/><br> polynomials in the two variables dening some algebraic curves and annihilating the two<br/><br> commuting elements. We show that for the elements from the 0chain subalgebra exactly<br/><br> one algebraic curve arises in the expansion of the determinant. Finally, we present several<br/><br> examples of computation of such algebraic curves and also make some observations on<br/><br> the properties of these curves.}, author = {Richter, Johan and Silvestrov, Sergei}, issn = {17365279}, keyword = {BurchnallChaundy theory,Heisenberg algebra}, language = {eng}, number = {4}, pages = {321328}, publisher = {Ashdin Publishing}, series = {Journal of Generalized Lie Theory and Applications}, title = {On algebraic curves for commuting elements in $q$Heisenberg algebras}, volume = {3}, year = {2009}, }