A Computational Approach to Examining Dixmier Conjecture in a Specific Case
Online First: 04/05/2026
Corressponding author's email:
hoangdv@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.2026.1912Keywords:
Algebra, Computer Algebra, Lie Algebra, Dixmier Conjecture, Maple softwareAbstract
Dixmier Conjecture on Weyl algebra is one of the central open problems in the field of Lie theory and non-commutative algebra. In this paper, by using the computer algebra system (Maple) we examine a particular instance of this conjecture involving two polynomial generators of relatively low degrees. In parallel, we also study a conjecture introduced in 1997 by Professor Nguyen Huu Anh, which shares deep structural similarities with Dixmier conjecture. Our research reveals a logical relationship between the two conjectures. From a computational perspective, we develop a computer program to systematically construct and analyze all polynomial pairs of degrees (6,9) whose Lie products are constants, thereby confirming the validity of the Dixmier Conjecture in this specific case. Our results contribute to a deeper understanding of the computational and theoretical boundaries of Dixmier conjecture and other related problems in non-commutative algebra.
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