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

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

2007-10-15

arxiv.org/abs/0710.2748v2

Journal of Algebra 321 (2009), pp. 1239-1255

Mathematics

Rings and Algebras

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

Scientific paper

10.1016/j.jalgebra.2008.10.021

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.

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