Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra
de Jeu, Marcel; Svensson, Christian; Silvestrov, Sergei (2007). Algebraic Curves for Commuting Elements in the q-deformed Heisenberg Algebra. Preprints in Mathematical Sciences (23)
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Unpublished
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English
Authors:
de Jeu, Marcel
;
Svensson, Christian
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
Research Group:
Non-commutative Geometry-lup-obsolete
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
Keywords:
q-deformed Heisenberg algebra ;
commuting elements ;
Burchnall-Chaundy eliminant construction ;
algebraic dependence
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