Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
Rings and Algebras
2009-01-14 v2 Quantum Algebra
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
Cite
@article{arxiv.0710.2748,
title = {Algebraic curves for commuting elements in the q-deformed Heisenberg algebra},
author = {Marcel de Jeu and Christian Svensson and Sergei Silvestrov},
journal= {arXiv preprint arXiv:0710.2748},
year = {2009}
}
Comments
18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra.