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

Research output: Contribution to journal › Article › peer-review

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

Access to Document

10.1080/00927872.2024.2407991

Cite this

@article{2135245110114e2381fea575033ddbbd,

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",

volume = "53",

pages = "1307--1319",

journal = "Communications in Algebra",

issn = "0092-7872",

number = "3",

}

TY - JOUR

T1 - Number of homogeneous components of counterexamples to the Dixmier conjecture

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

VL - 53

SP - 1307

EP - 1319

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -

Number of homogeneous components of counterexamples to the Dixmier conjecture

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this