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

Sección de Matemáticas

University of Buenos Aires
Pabellón 1-Ciudad Universitaria
Instituto Argentino de Matemática-CONICET
Instituto de Matemática y Ciencias Afines

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

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].

Idioma original	Inglés
Páginas (desde-hasta)	1307-1319
Número de páginas	13
Publicación	Communications in Algebra
Volumen	53
N.º	3
DOI	https://doi.org/10.1080/00927872.2024.2407991
Estado	Publicada - 2025

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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",

author = "Guccione, \{Jorge A.\} and Guccione, \{Juan J.\} and Christian Valqui",

note = "Publisher Copyright: {\textcopyright} 2024 Taylor \& Francis Group, LLC.",

year = "2025",

doi = "10.1080/00927872.2024.2407991",

language = "English",

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AU - Guccione, Jorge A.

AU - Guccione, Juan J.

AU - Valqui, Christian

PY - 2025

Y1 - 2025

N2 - 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].

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].

KW - Dixmier conjecture

KW - Newton polygon

KW - Weyl algebra

UR - https://www.scopus.com/pages/publications/85205870161

U2 - 10.1080/00927872.2024.2407991

DO - 10.1080/00927872.2024.2407991

M3 - Article

AN - SCOPUS:85205870161

SN - 0092-7872

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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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