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2020•Matematičeskie struktury i modelirovanieOpen access

AUTOISOMETRIES AND AUTOSIMILARITIES OF LIE ALGEBRA 𝒜(1) ⊕ ℛ2

М. Н. Подоксенов, V. V. Chernykh

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Abstract

We consider four-dimensional Lie algebra 𝒜(1) ⊕ ℛ2 endowed with Lorentzian scalar product. We find all the one-parameter groups of isometries and similarities, which are simultaneously automorphisms of Lie algebra, and also we find the conditions of existence of such one-parameter group. Conditions of existence are associated with the location of ideals with respect to isotropic cone.

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We consider four-dimensional Lie algebra 𝒜(1) ⊕ ℛ2 endowed with Lorentzian scalar product. We find all the one-parameter groups of isometries and similarities, which are simultaneously automorphisms of Lie algebra, and also we find the conditions of existence of such one-parameter group. Conditions of existence are associated with the location of ideals with respect to isotropic cone.

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Available abstract

We consider four-dimensional Lie algebra 𝒜(1) ⊕ ℛ2 endowed with Lorentzian scalar product. We find all the one-parameter groups of isometries and similarities, which are simultaneously automorphisms of Lie algebra, and also we find the conditions of existence of such one-parameter group. Conditions of existence are associated with the location of ideals with respect to isotropic cone.

Key concepts: Mathematics, Lie conformal algebra, Graded Lie algebra, Automorphism, Pure mathematics, Lie algebra, Lie group, Scalar (mathematics)

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