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A family of degenerate Lie algebras
Affiliation:1. Department of Neurology, Nanjing Drum Tower Hospital, Affiliated Hospital of Medical School, Nanjing University, Nanjing, China;2. Nanjing Drum Tower Hospital Clinical College of Traditional Chinese and Western Medicine, Nanjing University of Chinese Medicine, Nanjing, China;3. Nanjing Drum Tower Hospital Clinical College of Jiangsu University, Nanjing, China;4. Nanjing Drum Tower Hospital Clinical College of Nanjing Medical University, Nanjing, China;5. Jiangsu Key Laboratory of Molecular Medicine, Medical School of Nanjing University, Nanjing, China;6. Jiangsu Province Stroke Center for Diagnosis and Therapy, Nanjing, China;7. Nanjing Neuropsychiatry Clinic Medical Center, Nanjing, China;1. Department of Mathematics, Massachussets Institute of Technology, Cambridge, MA, USA;2. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain;3. Department of Mathematics, Cornell University, Ithaca, NY, USA;1. Laboratory of Geometry and Dynamical Systems, Department of Mathematics, EPSEB, Universitat Politècnica de Catalunya-IMTech in Barcelona and CRM Centre de Recerca Matemàtica, Campus de Bellaterra Edifici C, 08193 Bellaterra, Barcelona, Spain;2. BCAM Bilbao Center of Applied Mathematics, Mazarredo Zumarkalea, 14, 48009 Bilbao, Bizkaia, Spain;1. Centro de Matemática da Universidade do Porto (CMUP), Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, R. Campo Alegre, 687, 4169-007 Porto, Portugal;2. Center for Mathematical Analysis, Geometry and Dynamical Systems (CAMGSD), Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Abstract:
We show that almost all the real Lie algebras with only zero- and two-dimensional coadjoint orbits are degenerate in both the smooth and analytic category. The only exceptions are the already known cases (studied for example by Dufour and Weinstein).
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