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On algebraic curves for commuting elements in $q$-Heisenberg algebras
Lund University.ORCID iD: 0000-0003-3931-7358
Mälardalen University, School of Education, Culture and Communication. Lund University. (Matematik/tillämpad matematik)ORCID iD: 0000-0003-4554-6528
2009 (English)In: Journal of Generalized Lie Theory and Applications, ISSN 1736-5279, E-ISSN 1736-4337, Vol. 3, no 4, 321-328 p.Article in journal (Refereed) Published
Abstract [en]

In the present article we continue investigating the algebraic dependence of commutingelements in q-deformed Heisenberg algebras. We provide a simple proof that the0-chain subalgebra is a maximal commutative subalgebra when q is of free type and thatit coincides with the centralizer (commutant) of any one of its elements dierent fromthe scalar multiples of the unity. We review the Burchnall-Chaundy-type construction forproving algebraic dependence and obtaining corresponding algebraic curves for commutingelements in the q-deformed Heisenberg algebra by computing a certain determinantwith entries depending on two commuting variables and one of the generators. The coecients in front of the powers of the generator in the expansion of the determinant arepolynomials in the two variables dening some algebraic curves and annihilating the twocommuting elements. We show that for the elements from the 0-chain subalgebra exactlyone algebraic curve arises in the expansion of the determinant. Finally, we present severalexamples of computation of such algebraic curves and also make some observations onthe properties of these curves.

Place, publisher, year, edition, pages
2009. Vol. 3, no 4, 321-328 p.
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22069DOI: 10.4303/jglta/S090405OAI: oai:DiVA.org:mdh-22069DiVA: diva2:679249
Available from: 2013-12-14 Created: 2013-10-23 Last updated: 2016-12-27Bibliographically approved

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Publisher's full texthttp://dx.doi.org/10.4303/jglta/S090405

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