Testing isomorphism of complex Lie algebras

Tuan A. Nguyen; Vu A. Le; Thieu N. Vo

doi:10.1080/00927872.2025.2553026

Testing isomorphism of complex Lie algebras

Tuan A. Nguyen, Vu A. Le, Thieu N. Vo

Department of Computer Science

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

Abstract

This paper studies algorithms for testing isomorphism of Lie algebras over the field of complex numbers. First, we combine the so-called linearization method with effective Nullstellensatz to prove the existence of an algorithm that tests isomorphism of n-dimensional complex Lie algebras using singly-exponential arithmetic operations in n. Second, we construct more practical algorithms for testing isomorphism of complex Lie algebras, including those with parameters, by means of triangular decomposition. Several applications of the proposed algorithms are also discussed.

Original language	English
Journal	Communications in Algebra
Early online date	9 Sept 2025
DOIs	https://doi.org/10.1080/00927872.2025.2553026
Publication status	Published - 9 Sept 2025

Bibliographical note

Publisher Copyright:
© 2025 Taylor & Francis Group, LLC.

Acknowledgements

The authors would like to thank the referees for their constructive comments, which have significantly improved the presentation of the paper.

Funding

This research is supported by the project B2024-SPD-07.

Keywords

Algorithm
isomorphism testing
Lie algebra

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927872.2025.2553026

Cite this

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Testing isomorphism of complex Lie algebras

Abstract

Bibliographical note

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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