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Classification of Solvable Lie groups whose non-trivial coadjoint orbits are of Codimension $1$

Hieu Van Ha|Duong Quang Hoa|Vu Anh Le
대한수학회 (The Korean Mathematical Society)|2022.10|대한수학회논문집 (Communications of the KMS)|제37권 제4호|pp. 1181-1197|DOI 10.4134/CKMS.c210308

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참고문헌

키워드

MD-algebrascoadjoint orbitsclassification of Lie group
주제분류수학

초록

We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

Abstract

We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

참고문헌 (30)

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