A Computational Approach to Examining Dixmier Conjecture in a Specific Case: Online First: 04/05/2026

Van Hoang Dinh; Van Minh Man Nguyen

doi:10.54644/jte.2026.1912

Các tác giả

Van Hoang Dinh Ho Chi Minh City University of Technology and Engineering, Vietnam https://orcid.org/0009-0005-8471-0230
Van Minh Man Nguyen Mahidol University (MUSC), Bangkok 10400, Thailand https://orcid.org/0000-0002-8173-1969

Email tác giả liên hệ:

hoangdv@hcmute.edu.vn

DOI:

https://doi.org/10.54644/jte.2026.1912

Từ khóa:

Algebra, Computer Algebra, Lie Algebra, Dixmier Conjecture, Maple software

Tóm tắt

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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Tiểu sử của Tác giả

Van Hoang Dinh, Ho Chi Minh City University of Technology and Engineering, Vietnam

Van Hoang Dinh earned his Bachelor’s and Master’s degrees in Mathematics from Ho Chi Minh City University of Science in 2004 and 2008, respectively. He obtained his Ph.D. in Mathematics from the University of Antwerp, Belgium, in 2016. From 2017 to 2020, he served as a lecturer and researcher in Mathematics at the Faculty of Applied Sciences, Ho Chi Minh City University of Technology and Engineering (HCMUTE). Since 2021, he has been a faculty member at the Faculty of Advanced Education, HCMUTE.

Email: hoangdv@hcmute.edu.vn. ORCID: https://orcid.org/0009-0005-8471-0230

Van Minh Man Nguyen, Mahidol University (MUSC), Bangkok 10400, Thailand

Van Minh Man Nguyen is a full-time faculty member at Department of Mathematics, Faculty of Science, Mahidol University (MUSC), Bangkok, Thailand. Prior to joining MU, he served (from 1998 to 2016) in University of Technology, VNU-HCM, Ho Chi Minh City, Vietnam, as a lecturer in computational mathematics and statistics. He accomplished his Ph.D. degree in Statistics (2005) at Eindhoven University of Technology, Netherlands. His current research interests include computer algebra, discrete optimization, mathematical statistics, time series analytics, quality control and management, and environmental epidemiology.

Email: man.ngu@mahidol.ac.th. ORCID: https://orcid.org/0000-0002-8173-1969

Tài liệu tham khảo

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