Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
| Autor: | Christian Svensson, Sergei Silvestrov, Marcel de Jeu |
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| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Eliminant Laurent series Current algebra Algebraic dependence Mathematics - Rings and Algebras Differential operator Filtered algebra Algebra Rings and Algebras (math.RA) Mathematics - Quantum Algebra FOS: Mathematics 16S99 (Primary) 81S05 39A13 (Secondary) Algebra representation Quantum Algebra (math.QA) Cellular algebra Commuting elements Algebraic curve Algebra over a field q-Deformed Heisenberg algebra Mathematics |
| Zdroj: | Journal of Algebra. 321:1239-1255 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2008.10.021 |
| Popis: | 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. 18 pages, 2 figures, LaTeX. Final version with some improvements in presentation. To appear in Journal of Algebra. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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