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Issue: Tập 23, Số 6 (2026)
Section: Articles
DOI: 10.54607/hcmue.js.23.6.5211(2026)
Date Published: 30/06/2026
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Nguyen, M. T., Doan, L. M., & Nguyen, T. K. T. (2026). K-ORBITS OF SOLVABLE LIE GROUPS WHOSE LIE ALGEBRAS ARE SEVEN-DIMENSIONAL WITH FIVE-DIMENSIONAL NILRADICALS. Ho Chi Minh City University of Education Journal of Science, 23(6), 1492-1503. https://doi.org/10.54607/hcmue.js.23.6.5211(2026)

K-ORBITS OF SOLVABLE LIE GROUPS WHOSE LIE ALGEBRAS ARE SEVEN-DIMENSIONAL WITH FIVE-DIMENSIONAL NILRADICALS

Nguyen Minh Triet1, , Doan Le Minh1, Nguyen Thi Kim Tran1
1 Ho Chi Minh City University of Education, Vietnam

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Abstract

Kirillov’s orbit method is a fundamental tool for studying representations of Lie groups and Lie algebras, with coadjoint orbits playing a central role. This paper investigates the geometry of coadjoint orbits of connected, simply connected Lie groups whose associated Lie algebras are explicitly specified. Building on recent classification results for a particular family of seven-dimensional solvable Lie algebras with five-dimensional nilradicals, the study provides a constructive and explicit geometric description of the corresponding coadjoint orbits. The findings clarify the relationship among solvable Lie groups, their Lie algebras, and the geometric structures arising from them.

Keywords

coadjoint orbit, coadjoint representation, Lie algebra, Lie group, nilradical

Article Details

References

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