In the paper [1] the method is proposed to describe an affine-homogeneous real hypersurfaces of 3-dimensional complex space with use of the Lie algebras. Large family of homogeneous surfaces and the corresponding Lie algebras were obtained there. Under this the main difficulties are related to the 5-dimensional algebras, specifically, to the study of systems of quadratic equations describing such algebras. Below there is a description of the 5-dimensional matrix Lie algebras for homogeneous surfaces of type (0, ε), which is obtained in an Maple environment and can be considered as a complement to the result of [1].
homogeneous manifold, the Lie algebra, complex space, matrix Lie algebra.
УДК: 517.55+519.688
ИСПОЛЬЗОВАНИЕ КОМПЬЮТЕРНЫХ АЛГОРИТМОВ ПРИ РЕШЕНИИ СИСТЕМ КВАДРАТИЧНЫХ УРАВНЕНИЙ
The use computer algorithms for solving systems
of quadratic equations
ШиповскаяА.В.
ФГБОУ ВПО «Воронежский государственный архитектурно-строительный университет»
г. Воронеж, Россия
DOI: 10.12737/6772
Аннотация: В работе [1] предложен способ описания аффинно-однородных вещественных гиперповерхностей 3-мерного комплексного пространства с помощью алгебр Ли. Там же получено большое семейство однородных поверхностей и отвечающих им алгебр Ли. При этом основные трудности связаны с 5-мерными алгебрами, а именно, с исследованием систем квадратичных уравнений, описывающих такие алгебры. Ниже приводится описание 5-мерных матричных алгебр Ли для однородных поверхностей типа (0,ε), дополняющее результат [1] и полученное в среде Maple.
Summary:In the paper [1] the method is proposed to describe an affine-homogeneous real hypersurfaces of 3-dimensional complex space with use of the Lie algebras. Large family of homogeneous surfaces and the corresponding Lie algebras were obtained there. Under this the main difficulties are related to the 5-dimensional algebras, specifically, to the study of systems of quadratic equations describing such algebras. Below there is a description of the 5-dimensional matrix Lie algebras for homogeneous surfaces of type (0, ε), which is obtained in an Maple environment and can be considered as a complement to the result of [1].
Ключевые слова. Однородное многообразие, алгебра Ли, комплексное пространство, матричная алгебра Ли.
Keywords: homogeneous manifold, the Lie algebra, complex space, matrix Lie algebra.
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