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International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
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On holomorphic realizations of 5-dimensional Lie algebras A. V. Loboda Voronezh State Technical University |
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Abstract: An approach to the problem of describing holomorphically homogeneous real hypersurfaces of 3-dimensional complex spaces is discussed, connected with the Lie algebras of vector fields on such manifolds. After a series of papers by author, Fels-Kaup, Dubrov-Medvedev-The, only Levi-nondegenerate hypersurfaces are of interest in this problem for which the corresponding algebras are 5-dimensional and have full rank. The report realizes a scheme for constructing homogeneous surfaces starting from abstract algebras, proposed by E.Cartan and developed by Beloshapka-Kossovskiy. It is shown that most of the known complete list containing 67 types of 5-dimensional algebras can be realized only on degenerate surfaces or on affine-homogeneous tubes. New examples (not reducible to known ones) of holomorphically homogeneous real hypersurfaces are obtained. Language: English |
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