Classification of connected commutative locally Nash groups |
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| Institution: | 1. School of Sciences, Harbin Institute of Technology, Shenzhen, 518055, China;2. School of Sciences, Jiangnan University, Wuxi, 214122, China;3. UFR IM2AG, Uuiversité Grenoble Alpes, Saint Martin D''Hères, France;1. Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada;2. University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, S4S 0A2, Canada;1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh 160014, India;2. Department of Mathematical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Mohali (Punjab) 140306, India;1. Universidad Autónoma de Ciudad Juárez, Av. Plutarco Elías Calles, 32310 Ciudad Juárez, Chih., Mexico;2. 500 W University Ave, Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX, 79968, USA;3. Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd. Marcelino García Barragán, 44430, Guadalajara, Jalisco, Mexico |
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| Abstract: | In this article, we classify connected commutative (locally) Nash groups, which is a continuation of our previous work on the classification of abelian Nash manifolds. Our results generalize the classification of the one-dimensional case by Madden-Stanton and the two-dimensional case by Baro-Vicente-Otero. Moreover, we determine the affineness and toroidal affineness of a connected commutative Nash group. |
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| Keywords: | Locally Nash groups Classification |
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