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

M. de Jeu; Charlotte Svensson; Sergei Silvestrov

doi:10.1016/j.jalgebra.2008.10.021

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

M. de Jeu, Charlotte Svensson, Sergei Silvestrov

Mathematics (Faculty of Engineering)

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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	https://doi.org/10.1016/j.jalgebra.2008.10.021
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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10.1016/j.jalgebra.2008.10.021

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title = "Algebraic curves for commuting elements in the q-deformed Heisenberg 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. (C) 2008 Elsevier Inc. All rights reserved.",

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T1 - Algebraic curves for commuting elements in the q-deformed Heisenberg algebra

AU - de Jeu, M.

AU - Svensson, Charlotte

AU - Silvestrov, Sergei

PY - 2009

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N2 - 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.

AB - 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.

KW - q-Deformed Heisenberg algebra

KW - Commuting elements

KW - Algebraic dependence

KW - Eliminant

KW - DIFFERENCE OPERATORS

U2 - 10.1016/j.jalgebra.2008.10.021

DO - 10.1016/j.jalgebra.2008.10.021

M3 - Article

SN - 0021-8693

VL - 321

SP - 1239

EP - 1255

JO - Journal of Algebra

JF - Journal of Algebra

IS - 4

ER -

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

Abstract

Subject classification (UKÄ)

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