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The aim is to explore the existence of characteristically nilpotent Lie algebras with flat coadjoint orbits.

March 29, 2026Journal of Lie theoryOpen Access

Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits

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The aim is to explore the existence of characteristically nilpotent Lie algebras with flat coadjoint orbits.
Constructed a two-parameter family of nilpotent Lie groups in dimension 11.
Analyzed the square-integrable representations modulo the center for these groups.
Investigated the quotient of these groups by their center regarding the existence of dilations.
Developed a family of Lie groups G(, ) that admit square-integrable representations.
The quotient G(, )/Z does not allow a family of dilations, which is significant for understanding their structure.

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Constructs a two-parameter family of nilpotent Lie groups with square-integrable representations, indicating new insights into their properties.

Burde et al. (2025) studied this question.

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Constructs a two-parameter family of nilpotent Lie groups with square-integrable representations, indicating new insights into their properties.