The Dixmier Conjecture and the shape of possible counterexamples

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

doi:10.1016/j.jalgebra.2013.10.011

The Dixmier Conjecture and the shape of possible counterexamples

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

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Abstract

We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that B>. 15, where B is the minimum of the greatest common divisor of the total degrees of P and Q, where (P, Q) runs over the counterexamples of the Dixmier Conjecture.

Original language	English
Pages (from-to)	581-633
Number of pages	53
Journal	Journal of Algebra
Volume	399
DOIs	https://doi.org/10.1016/j.jalgebra.2013.10.011
State	Published - 1 Feb 2014

Keywords

Dixmier Conjecture
Weyl algebra

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10.1016/j.jalgebra.2013.10.011

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title = "The Dixmier Conjecture and the shape of possible counterexamples",

abstract = "We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that B>. 15, where B is the minimum of the greatest common divisor of the total degrees of P and Q, where (P, Q) runs over the counterexamples of the Dixmier Conjecture.",

keywords = "Dixmier Conjecture, Weyl algebra",

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

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AU - Guccione, Jorge A.

AU - Guccione, Juan J.

AU - Valqui, Christian

PY - 2014/2/1

Y1 - 2014/2/1

N2 - We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that B>. 15, where B is the minimum of the greatest common divisor of the total degrees of P and Q, where (P, Q) runs over the counterexamples of the Dixmier Conjecture.

AB - We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that B>. 15, where B is the minimum of the greatest common divisor of the total degrees of P and Q, where (P, Q) runs over the counterexamples of the Dixmier Conjecture.

KW - Dixmier Conjecture

KW - Weyl algebra

UR - http://www.scopus.com/inward/record.url?scp=84887230402&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2013.10.011

DO - 10.1016/j.jalgebra.2013.10.011

M3 - Article

AN - SCOPUS:84887230402

SN - 0021-8693

VL - 399

SP - 581

EP - 633

JO - Journal of Algebra

JF - Journal of Algebra

ER -

The Dixmier Conjecture and the shape of possible counterexamples

Abstract

Keywords

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