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Algebraic curves for commuting elements in the $q$-deformed Heisenberg algebra
Leiden University, Netherlands .
Lund University.
Lund University. (Matematik/tillämpad matematik)ORCID iD: 0000-0003-4554-6528
2009 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 321, no 4, p. 1239-1255Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 321, no 4, p. 1239-1255
Keywords [en]
q-Deformed Heisenberg algebra, Commuting elements, Algebraic dependence, Eliminant
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22086DOI: 10.1016/j.jalgebra.2008.10.021ISI: 000263333400008Scopus ID: 2-s2.0-58149157792OAI: oai:DiVA.org:mdh-22086DiVA, id: diva2:682237
Available from: 2013-12-26 Created: 2013-10-23 Last updated: 2017-12-06Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1016/j.jalgebra.2008.10.021

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Silvestrov, Sergei

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