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

Research paper by Marcel de Jeu, Christian Svensson, Sergei Silvestrov

Indexed on: 18 Nov '08Published on: 18 Nov '08Published in: Mathematics - Rings and Algebras



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.