Number of homogeneous components of counterexamples to the Dixmier conjecture

Jorge A. Guccione; Juan J. Guccione; Christian Valqui

doi:10.1080/00927872.2024.2407991

Number of homogeneous components of counterexamples to the Dixmier conjecture

Jorge A. Guccione, Juan J. Guccione, Christian Valqui

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Abstract

Assume that P and Q are elements of A₁ satisfying (Formula presented.). The Dixmier Conjecture for A₁ says that they always generate A₁. We show that if P is a sum of not more than 4 homogeneous elements of A₁ then P and Q generate A₁, which generalizes the main result in [10].

Original language	English
Pages (from-to)	1307-1319
Number of pages	13
Journal	Communications in Algebra
Volume	53
Issue number	3
DOIs	https://doi.org/10.1080/00927872.2024.2407991
State	Published - 2025

Keywords

Dixmier conjecture
Newton polygon
Weyl algebra

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10.1080/00927872.2024.2407991

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title = "Number of homogeneous components of counterexamples to the Dixmier conjecture",

abstract = "Assume that P and Q are elements of A1 satisfying (Formula presented.). The Dixmier Conjecture for A1 says that they always generate A1. We show that if P is a sum of not more than 4 homogeneous elements of A1 then P and Q generate A1, which generalizes the main result in [10].",

keywords = "Dixmier conjecture, Newton polygon, Weyl algebra",

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AU - Guccione, Juan J.

AU - Valqui, Christian

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AB - Assume that P and Q are elements of A1 satisfying (Formula presented.). The Dixmier Conjecture for A1 says that they always generate A1. We show that if P is a sum of not more than 4 homogeneous elements of A1 then P and Q generate A1, which generalizes the main result in [10].

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KW - Newton polygon

KW - Weyl algebra

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M3 - Article

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SP - 1307

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JO - Communications in Algebra

JF - Communications in Algebra

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ER -

Number of homogeneous components of counterexamples to the Dixmier conjecture

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