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. (C) 2008 Elsevier Inc. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 1239-1255 |
| Journal | Journal of Algebra |
| Volume | 321 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2009 |
Subject classification (UKÄ)
- Mathematical Sciences
Free keywords
- q-Deformed Heisenberg algebra
- Commuting elements
- Algebraic dependence
- Eliminant
- DIFFERENCE OPERATORS
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