Algebraic curves for commuting elements in the q-deformed Heisenberg algebra

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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.
18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra.

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Rings and Algebras, Quantum Algebra, 16S99 (Primary) 81S05, 39A13 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/215562

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.2748
 http://arxiv.org/abs/0710.2748
 Journal of Algebra 321 (2009), pp. 1239-1255
 doi:10.1016/j.jalgebra.2008.10.021

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arXiv