Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
Marcel de Jeu, Christian Svensson, and Sergei Silvestrov
TL;DR
This paper extends the classical algebraic curve construction for commuting differential operators to the q-deformed Heisenberg algebra, providing new insights into its structure and eigenspace dimensions.
Contribution
It generalizes the eliminant construction to the q-deformed setting, establishing annihilating curves for commuting elements under certain conditions.
Findings
Constructed algebraic curves for commuting elements in the q-deformed algebra
Provided estimates on eigenspace dimensions of algebra elements
Extended classical methods to a q-deformed algebraic context
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra · Algebraic structures and combinatorial models